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3",[581,905,907,926,978],{"className":906,"ariaHidden":622},[670],[581,908,910,914,917,920,923],{"className":909},[674],[581,911],{"className":912,"style":913},[678],"height:0.6444em;",[581,915,885],{"className":916},[687],[581,918],{"className":919,"style":717},[705],[581,921,632],{"className":922},[721],[581,924],{"className":925,"style":717},[705],[581,927,929,933,969,972,975],{"className":928},[674],[581,930],{"className":931,"style":932},[678],"height:0.8141em;",[581,934,936,939],{"className":935},[687],[581,937,893],{"className":938},[687],[581,940,943],{"className":941},[942],"msupsub",[581,944,946],{"className":945},[745],[581,947,949],{"className":948},[750],[581,950,952],{"className":951,"style":932},[754],[581,953,955,959],{"style":954},"top:-3.063em;margin-right:0.05em;",[581,956],{"className":957,"style":958},[762],"height:2.7em;",[581,960,966],{"className":961},[962,963,964,965],"sizing","reset-size6","size3","mtight",[581,967,893],{"className":968},[687,965],[581,970],{"className":971,"style":817},[705],[581,973,642],{"className":974},[821],[581,976],{"className":977,"style":817},[705],[581,979,981,984],{"className":980},[674],[581,982],{"className":983,"style":913},[678],[581,985,900],{"className":986},[687]," und ",[581,989,991,1018],{"className":990},[588],[581,992,994],{"className":993},[592],[594,995,996],{"xmlns":596},[599,997,998,1015],{},[602,999,1000,1003,1005,1007,1009],{},[883,1001,1002],{},"18",[610,1004,632],{},[883,1006,893],{},[610,1008,642],{},[889,1010,1011,1013],{},[883,1012,900],{},[883,1014,893],{},[663,1016,1017],{"encoding":665},"18 = 2 \\cdot 3^2",[581,1019,1021,1039,1057],{"className":1020,"ariaHidden":622},[670],[581,1022,1024,1027,1030,1033,1036],{"className":1023},[674],[581,1025],{"className":1026,"style":913},[678],[581,1028,1002],{"className":1029},[687],[581,1031],{"className":1032,"style":717},[705],[581,1034,632],{"className":1035},[721],[581,1037],{"className":1038,"style":717},[705],[581,1040,1042,1045,1048,1051,1054],{"className":1041},[674],[581,1043],{"className":1044,"style":913},[678],[581,1046,893],{"className":1047},[687],[581,1049],{"className":1050,"style":817},[705],[581,1052,642],{"className":1053},[821],[581,1055],{"className":1056,"style":817},[705],[581,1058,1060,1063],{"className":1059},[674],[581,1061],{"className":1062,"style":932},[678],[581,1064,1066,1069],{"className":1065},[687],[581,1067,900],{"className":1068},[687],[581,1070,1072],{"className":1071},[942],[581,1073,1075],{"className":1074},[745],[581,1076,1078],{"className":1077},[750],[581,1079,1081],{"className":1080,"style":932},[754],[581,1082,1083,1086],{"style":954},[581,1084],{"className":1085,"style":958},[762],[581,1087,1089],{"className":1088},[962,963,964,965],[581,1090,893],{"className":1091},[687,965],":",[581,1094,1096],{"className":1095},[584],[581,1097,1099,1176],{"className":1098},[588],[581,1100,1102],{"className":1101},[592],[594,1103,1104],{"xmlns":596,"display":597},[599,1105,1106,1173],{},[602,1107,1108,1110,1112,1114,1116,1118,1120,1122,1124,1126,1128,1130,1132,1135,1138,1140,1142,1144,1146,1148,1150,1152,1154,1160,1162,1168,1170],{},[605,1109,649],{"mathvariant":607},[610,1111,612],{},[610,1113,616],{"stretchy":615},[883,1115,885],{},[610,1117,623],{"separator":622},[883,1119,1002],{},[610,1121,629],{"stretchy":615},[610,1123,632],{},[883,1125,893],{},[610,1127,642],{},[883,1129,900],{},[610,1131,632],{},[883,1133,1134],{},"6",[705,1136],{"width":1137},"2em",[605,1139,608],{"mathvariant":607},[610,1141,612],{},[610,1143,616],{"stretchy":615},[883,1145,885],{},[610,1147,623],{"separator":622},[883,1149,1002],{},[610,1151,629],{"stretchy":615},[610,1153,632],{},[889,1155,1156,1158],{},[883,1157,893],{},[883,1159,893],{},[610,1161,642],{},[889,1163,1164,1166],{},[883,1165,900],{},[883,1167,893],{},[610,1169,632],{},[883,1171,1172],{},"36",[663,1174,1175],{"encoding":665},"\\operatorname{ggT}(12, 18) = 2 \\cdot 3 = 6 \\qquad \\operatorname{kgV}(12, 18) = 2^2 \\cdot 3^2 = 36",[581,1177,1179,1218,1236,1254,1303,1349,1393],{"className":1178,"ariaHidden":622},[670],[581,1180,1182,1185,1191,1194,1197,1200,1203,1206,1209,1212,1215],{"className":1181},[674],[581,1183],{"className":1184,"style":679},[678],[581,1186,1188],{"className":1187},[683],[581,1189,649],{"className":1190},[687,688],[581,1192,616],{"className":1193},[693],[581,1195,885],{"className":1196},[687],[581,1198,623],{"className":1199},[701],[581,1201],{"className":1202,"style":706},[705],[581,1204,1002],{"className":1205},[687],[581,1207,629],{"className":1208},[713],[581,1210],{"className":1211,"style":717},[705],[581,1213,632],{"className":1214},[721],[581,1216],{"className":1217,"style":717},[705],[581,1219,1221,1224,1227,1230,1233],{"className":1220},[674],[581,1222],{"className":1223,"style":913},[678],[581,1225,893],{"className":1226},[687],[581,1228],{"className":1229,"style":817},[705],[581,1231,642],{"className":1232},[821],[581,1234],{"className":1235,"style":817},[705],[581,1237,1239,1242,1245,1248,1251],{"className":1238},[674],[581,1240],{"className":1241,"style":913},[678],[581,1243,900],{"className":1244},[687],[581,1246],{"className":1247,"style":717},[705],[581,1249,632],{"className":1250},[721],[581,1252],{"className":1253,"style":717},[705],[581,1255,1257,1260,1263,1267,1270,1276,1279,1282,1285,1288,1291,1294,1297,1300],{"className":1256},[674],[581,1258],{"className":1259,"style":679},[678],[581,1261,1134],{"className":1262},[687],[581,1264],{"className":1265,"style":1266},[705],"margin-right:2em;",[581,1268],{"className":1269,"style":706},[705],[581,1271,1273],{"className":1272},[683],[581,1274,608],{"className":1275,"style":689},[687,688],[581,1277,616],{"className":1278},[693],[581,1280,885],{"className":1281},[687],[581,1283,623],{"className":1284},[701],[581,1286],{"className":1287,"style":706},[705],[581,1289,1002],{"className":1290},[687],[581,1292,629],{"className":1293},[713],[581,1295],{"className":1296,"style":717},[705],[581,1298,632],{"className":1299},[721],[581,1301],{"className":1302,"style":717},[705],[581,1304,1306,1310,1340,1343,1346],{"className":1305},[674],[581,1307],{"className":1308,"style":1309},[678],"height:0.8641em;",[581,1311,1313,1316],{"className":1312},[687],[581,1314,893],{"className":1315},[687],[581,1317,1319],{"className":1318},[942],[581,1320,1322],{"className":1321},[745],[581,1323,1325],{"className":1324},[750],[581,1326,1328],{"className":1327,"style":1309},[754],[581,1329,1331,1334],{"style":1330},"top:-3.113em;margin-right:0.05em;",[581,1332],{"className":1333,"style":958},[762],[581,1335,1337],{"className":1336},[962,963,964,965],[581,1338,893],{"className":1339},[687,965],[581,1341],{"className":1342,"style":817},[705],[581,1344,642],{"className":1345},[821],[581,1347],{"className":1348,"style":817},[705],[581,1350,1352,1355,1384,1387,1390],{"className":1351},[674],[581,1353],{"className":1354,"style":1309},[678],[581,1356,1358,1361],{"className":1357},[687],[581,1359,900],{"className":1360},[687],[581,1362,1364],{"className":1363},[942],[581,1365,1367],{"className":1366},[745],[581,1368,1370],{"className":1369},[750],[581,1371,1373],{"className":1372,"style":1309},[754],[581,1374,1375,1378],{"style":1330},[581,1376],{"className":1377,"style":958},[762],[581,1379,1381],{"className":1380},[962,963,964,965],[581,1382,893],{"className":1383},[687,965],[581,1385],{"className":1386,"style":717},[705],[581,1388,632],{"className":1389},[721],[581,1391],{"className":1392,"style":717},[705],[581,1394,1396,1399],{"className":1395},[674],[581,1397],{"className":1398,"style":913},[678],[581,1400,1172],{"className":1401},[687],[565,1403,1404,1405,1523],{},"Probe mit der Formel: ",[581,1406,1408,1439],{"className":1407},[588],[581,1409,1411],{"className":1410},[592],[594,1412,1413],{"xmlns":596},[599,1414,1415,1436],{},[602,1416,1417,1419,1421,1423,1425,1428,1430,1432,1434],{},[883,1418,1134],{},[610,1420,642],{},[883,1422,1172],{},[610,1424,632],{},[883,1426,1427],{},"216",[610,1429,632],{},[883,1431,885],{},[610,1433,642],{},[883,1435,1002],{},[663,1437,1438],{"encoding":665},"6 \\cdot 36 = 216 = 12 \\cdot 18",[581,1440,1442,1460,1478,1496,1514],{"className":1441,"ariaHidden":622},[670],[581,1443,1445,1448,1451,1454,1457],{"className":1444},[674],[581,1446],{"className":1447,"style":913},[678],[581,1449,1134],{"className":1450},[687],[581,1452],{"className":1453,"style":817},[705],[581,1455,642],{"className":1456},[821],[581,1458],{"className":1459,"style":817},[705],[581,1461,1463,1466,1469,1472,1475],{"className":1462},[674],[581,1464],{"className":1465,"style":913},[678],[581,1467,1172],{"className":1468},[687],[581,1470],{"className":1471,"style":717},[705],[581,1473,632],{"className":1474},[721],[581,1476],{"className":1477,"style":717},[705],[581,1479,1481,1484,1487,1490,1493],{"className":1480},[674],[581,1482],{"className":1483,"style":913},[678],[581,1485,1427],{"className":1486},[687],[581,1488],{"className":1489,"style":717},[705],[581,1491,632],{"className":1492},[721],[581,1494],{"className":1495,"style":717},[705],[581,1497,1499,1502,1505,1508,1511],{"className":1498},[674],[581,1500],{"className":1501,"style":913},[678],[581,1503,885],{"className":1504},[687],[581,1506],{"className":1507,"style":817},[705],[581,1509,642],{"className":1510},[821],[581,1512],{"className":1513,"style":817},[705],[581,1515,1517,1520],{"className":1516},[674],[581,1518],{"className":1519,"style":913},[678],[581,1521,1002],{"className":1522},[687],".",[565,1525,1526,1527,987,1556,1584,1585,1670],{},"Das kgV von ",[581,1528,1530,1544],{"className":1529},[588],[581,1531,1533],{"className":1532},[592],[594,1534,1535],{"xmlns":596},[599,1536,1537,1542],{},[602,1538,1539],{},[883,1540,1541],{},"8",[663,1543,1541],{"encoding":665},[581,1545,1547],{"className":1546,"ariaHidden":622},[670],[581,1548,1550,1553],{"className":1549},[674],[581,1551],{"className":1552,"style":913},[678],[581,1554,1541],{"className":1555},[687],[581,1557,1559,1572],{"className":1558},[588],[581,1560,1562],{"className":1561},[592],[594,1563,1564],{"xmlns":596},[599,1565,1566,1570],{},[602,1567,1568],{},[883,1569,885],{},[663,1571,885],{"encoding":665},[581,1573,1575],{"className":1574,"ariaHidden":622},[670],[581,1576,1578,1581],{"className":1577},[674],[581,1579],{"className":1580,"style":913},[678],[581,1582,885],{"className":1583},[687]," über den ggT: ",[581,1586,1588,1619],{"className":1587},[588],[581,1589,1591],{"className":1590},[592],[594,1592,1593],{"xmlns":596},[599,1594,1595,1616],{},[602,1596,1597,1599,1601,1603,1605,1607,1609,1611,1613],{},[605,1598,649],{"mathvariant":607},[610,1600,612],{},[610,1602,616],{"stretchy":615},[883,1604,1541],{},[610,1606,623],{"separator":622},[883,1608,885],{},[610,1610,629],{"stretchy":615},[610,1612,632],{},[883,1614,1615],{},"4",[663,1617,1618],{"encoding":665},"\\operatorname{ggT}(8, 12) = 4",[581,1620,1622,1661],{"className":1621,"ariaHidden":622},[670],[581,1623,1625,1628,1634,1637,1640,1643,1646,1649,1652,1655,1658],{"className":1624},[674],[581,1626],{"className":1627,"style":679},[678],[581,1629,1631],{"className":1630},[683],[581,1632,649],{"className":1633},[687,688],[581,1635,616],{"className":1636},[693],[581,1638,1541],{"className":1639},[687],[581,1641,623],{"className":1642},[701],[581,1644],{"className":1645,"style":706},[705],[581,1647,885],{"className":1648},[687],[581,1650,629],{"className":1651},[713],[581,1653],{"className":1654,"style":717},[705],[581,1656,632],{"className":1657},[721],[581,1659],{"className":1660,"style":717},[705],[581,1662,1664,1667],{"className":1663},[674],[581,1665],{"className":1666,"style":913},[678],[581,1668,1615],{"className":1669},[687],", also",[581,1672,1674],{"className":1673},[584],[581,1675,1677,1722],{"className":1676},[588],[581,1678,1680],{"className":1679},[592],[594,1681,1682],{"xmlns":596,"display":597},[599,1683,1684,1719],{},[602,1685,1686,1688,1690,1692,1694,1696,1698,1700,1702,1714,1716],{},[605,1687,608],{"mathvariant":607},[610,1689,612],{},[610,1691,616],{"stretchy":615},[883,1693,1541],{},[610,1695,623],{"separator":622},[883,1697,885],{},[610,1699,629],{"stretchy":615},[610,1701,632],{},[634,1703,1704,1712],{},[602,1705,1706,1708,1710],{},[883,1707,1541],{},[610,1709,642],{},[883,1711,885],{},[883,1713,1615],{},[610,1715,632],{},[883,1717,1718],{},"24",[663,1720,1721],{"encoding":665},"\\operatorname{kgV}(8, 12) = \\frac{8 \\cdot 12}{4} = 24",[581,1723,1725,1764,1856],{"className":1724,"ariaHidden":622},[670],[581,1726,1728,1731,1737,1740,1743,1746,1749,1752,1755,1758,1761],{"className":1727},[674],[581,1729],{"className":1730,"style":679},[678],[581,1732,1734],{"className":1733},[683],[581,1735,608],{"className":1736,"style":689},[687,688],[581,1738,616],{"className":1739},[693],[581,1741,1541],{"className":1742},[687],[581,1744,623],{"className":1745},[701],[581,1747],{"className":1748,"style":706},[705],[581,1750,885],{"className":1751},[687],[581,1753,629],{"className":1754},[713],[581,1756],{"className":1757,"style":717},[705],[581,1759,632],{"className":1760},[721],[581,1762],{"className":1763,"style":717},[705],[581,1765,1767,1771,1847,1850,1853],{"className":1766},[674],[581,1768],{"className":1769,"style":1770},[678],"height:2.0074em;vertical-align:-0.686em;",[581,1772,1774,1777,1844],{"className":1773},[687],[581,1775],{"className":1776},[693,738],[581,1778,1780],{"className":1779},[634],[581,1781,1783,1835],{"className":1782},[745,746],[581,1784,1786,1832],{"className":1785},[750],[581,1787,1790,1801,1809],{"className":1788,"style":1789},[754],"height:1.3214em;",[581,1791,1792,1795],{"style":758},[581,1793],{"className":1794,"style":763},[762],[581,1796,1798],{"className":1797},[687],[581,1799,1615],{"className":1800},[687],[581,1802,1803,1806],{"style":793},[581,1804],{"className":1805,"style":763},[762],[581,1807],{"className":1808,"style":801},[800],[581,1810,1811,1814],{"style":804},[581,1812],{"className":1813,"style":763},[762],[581,1815,1817,1820,1823,1826,1829],{"className":1816},[687],[581,1818,1541],{"className":1819},[687],[581,1821],{"className":1822,"style":817},[705],[581,1824,642],{"className":1825},[821],[581,1827],{"className":1828,"style":817},[705],[581,1830,885],{"className":1831},[687],[581,1833,832],{"className":1834},[831],[581,1836,1838],{"className":1837},[750],[581,1839,1842],{"className":1840,"style":1841},[754],"height:0.686em;",[581,1843],{},[581,1845],{"className":1846},[713,738],[581,1848],{"className":1849,"style":717},[705],[581,1851,632],{"className":1852},[721],[581,1854],{"className":1855,"style":717},[705],[581,1857,1859,1862],{"className":1858},[674],[581,1860],{"className":1861,"style":913},[678],[581,1863,1718],{"className":1864},[687],[565,1866,1867,1868,1897,1898,1901,1902,1987,1988,1523],{},"Haben zwei Zahlen keinen gemeinsamen Teiler außer ",[581,1869,1871,1885],{"className":1870},[588],[581,1872,1874],{"className":1873},[592],[594,1875,1876],{"xmlns":596},[599,1877,1878,1883],{},[602,1879,1880],{},[883,1881,1882],{},"1",[663,1884,1882],{"encoding":665},[581,1886,1888],{"className":1887,"ariaHidden":622},[670],[581,1889,1891,1894],{"className":1890},[674],[581,1892],{"className":1893,"style":913},[678],[581,1895,1882],{"className":1896},[687]," (sie sind ",[569,1899,1900],{},"teilerfremd","), ist das kgV einfach ihr Produkt: ",[581,1903,1905,1936],{"className":1904},[588],[581,1906,1908],{"className":1907},[592],[594,1909,1910],{"xmlns":596},[599,1911,1912,1933],{},[602,1913,1914,1916,1918,1920,1922,1924,1927,1929,1931],{},[605,1915,649],{"mathvariant":607},[610,1917,612],{},[610,1919,616],{"stretchy":615},[883,1921,1615],{},[610,1923,623],{"separator":622},[883,1925,1926],{},"9",[610,1928,629],{"stretchy":615},[610,1930,632],{},[883,1932,1882],{},[663,1934,1935],{"encoding":665},"\\operatorname{ggT}(4, 9) = 1",[581,1937,1939,1978],{"className":1938,"ariaHidden":622},[670],[581,1940,1942,1945,1951,1954,1957,1960,1963,1966,1969,1972,1975],{"className":1941},[674],[581,1943],{"className":1944,"style":679},[678],[581,1946,1948],{"className":1947},[683],[581,1949,649],{"className":1950},[687,688],[581,1952,616],{"className":1953},[693],[581,1955,1615],{"className":1956},[687],[581,1958,623],{"className":1959},[701],[581,1961],{"className":1962,"style":706},[705],[581,1964,1926],{"className":1965},[687],[581,1967,629],{"className":1968},[713],[581,1970],{"className":1971,"style":717},[705],[581,1973,632],{"className":1974},[721],[581,1976],{"className":1977,"style":717},[705],[581,1979,1981,1984],{"className":1980},[674],[581,1982],{"className":1983,"style":913},[678],[581,1985,1882],{"className":1986},[687],", ",[581,1989,1991,2021],{"className":1990},[588],[581,1992,1994],{"className":1993},[592],[594,1995,1996],{"xmlns":596},[599,1997,1998,2018],{},[602,1999,2000,2002,2004,2006,2008,2010,2012,2014,2016],{},[605,2001,608],{"mathvariant":607},[610,2003,612],{},[610,2005,616],{"stretchy":615},[883,2007,1615],{},[610,2009,623],{"separator":622},[883,2011,1926],{},[610,2013,629],{"stretchy":615},[610,2015,632],{},[883,2017,1172],{},[663,2019,2020],{"encoding":665},"\\operatorname{kgV}(4, 9) = 36",[581,2022,2024,2063],{"className":2023,"ariaHidden":622},[670],[581,2025,2027,2030,2036,2039,2042,2045,2048,2051,2054,2057,2060],{"className":2026},[674],[581,2028],{"className":2029,"style":679},[678],[581,2031,2033],{"className":2032},[683],[581,2034,608],{"className":2035,"style":689},[687,688],[581,2037,616],{"className":2038},[693],[581,2040,1615],{"className":2041},[687],[581,2043,623],{"className":2044},[701],[581,2046],{"className":2047,"style":706},[705],[581,2049,1926],{"className":2050},[687],[581,2052,629],{"className":2053},[713],[581,2055],{"className":2056,"style":717},[705],[581,2058,632],{"className":2059},[721],[581,2061],{"className":2062,"style":717},[705],[581,2064,2066,2069],{"className":2065},[674],[581,2067],{"className":2068,"style":913},[678],[581,2070,1172],{"className":2071},[687],[560,2073,2075],{"id":2074},"typische-fehler","Typische Fehler",[2077,2078,2079,2083,2201],"ul",{},[2080,2081,2082],"li",{},"ggT und kgV verwechseln: Der ggT ist höchstens so groß wie die kleinere Zahl, das kgV mindestens so groß wie die größere.",[2080,2084,2085,2086,987,2114,2142,2143,2171,2172,1523],{},"Als Hauptnenner einfach das Produkt nehmen: Das ist zwar ein gemeinsames Vielfaches, aber oft nicht das kleinste. Für ",[581,2087,2089,2102],{"className":2088},[588],[581,2090,2092],{"className":2091},[592],[594,2093,2094],{"xmlns":596},[599,2095,2096,2100],{},[602,2097,2098],{},[883,2099,1541],{},[663,2101,1541],{"encoding":665},[581,2103,2105],{"className":2104,"ariaHidden":622},[670],[581,2106,2108,2111],{"className":2107},[674],[581,2109],{"className":2110,"style":913},[678],[581,2112,1541],{"className":2113},[687],[581,2115,2117,2130],{"className":2116},[588],[581,2118,2120],{"className":2119},[592],[594,2121,2122],{"xmlns":596},[599,2123,2124,2128],{},[602,2125,2126],{},[883,2127,885],{},[663,2129,885],{"encoding":665},[581,2131,2133],{"className":2132,"ariaHidden":622},[670],[581,2134,2136,2139],{"className":2135},[674],[581,2137],{"className":2138,"style":913},[678],[581,2140,885],{"className":2141},[687]," reicht ",[581,2144,2146,2159],{"className":2145},[588],[581,2147,2149],{"className":2148},[592],[594,2150,2151],{"xmlns":596},[599,2152,2153,2157],{},[602,2154,2155],{},[883,2156,1718],{},[663,2158,1718],{"encoding":665},[581,2160,2162],{"className":2161,"ariaHidden":622},[670],[581,2163,2165,2168],{"className":2164},[674],[581,2166],{"className":2167,"style":913},[678],[581,2169,1718],{"className":2170},[687]," statt ",[581,2173,2175,2189],{"className":2174},[588],[581,2176,2178],{"className":2177},[592],[594,2179,2180],{"xmlns":596},[599,2181,2182,2187],{},[602,2183,2184],{},[883,2185,2186],{},"96",[663,2188,2186],{"encoding":665},[581,2190,2192],{"className":2191,"ariaHidden":622},[670],[581,2193,2195,2198],{"className":2194},[674],[581,2196],{"className":2197,"style":913},[678],[581,2199,2186],{"className":2200},[687],[2080,2202,2203,2204,1523],{},"Die Formel auf drei Zahlen übertragen: Für drei oder mehr Zahlen gilt sie so ",[569,2205,2206],{},"nicht",{"title":2208,"searchDepth":2209,"depth":2209,"links":2210},"",2,[2211,2212,2213],{"id":562,"depth":2209,"text":563},{"id":865,"depth":2209,"text":866},{"id":2074,"depth":2209,"text":2075},[2215,2221,2223,2225,2227,2229,2231,2233,2235,2237,2239,2241,2243,2245,2247,2249],{"lhs":2216,"rhs":2217,"where":2218},"gcd(a, b)*lcm(a, b)","a*b",{"a":2219,"b":2220},12,18,{"lhs":2222,"rhs":1134},"gcd(12, 18)",{"lhs":2224,"rhs":1172},"lcm(12, 18)",{"lhs":2226,"rhs":1427},"6*36",{"lhs":2228,"rhs":1427},"12*18",{"lhs":2230,"rhs":885},"2^2*3",{"lhs":2232,"rhs":1002},"2*3^2",{"lhs":2234,"rhs":1134},"2*3",{"lhs":2236,"rhs":1172},"2^2*3^2",{"lhs":2238,"rhs":1615},"gcd(8, 12)",{"lhs":2240,"rhs":1718},"8*12\u002F4",{"lhs":2242,"rhs":1718},"lcm(8, 12)",{"lhs":2244,"rhs":2186},"8*12",{"lhs":2246,"rhs":1882},"gcd(4, 9)",{"lhs":2248,"rhs":1172},"lcm(4, 9)",{"lhs":2216,"rhs":2217,"where":2250},{"a":2251,"b":2252},4,9,"a, b \\in \\mathbb{N},\\ a, b \\geq 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b \\in \\mathbb{N},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b \\geq 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","gcd-lcm","\\operatorname{ggT}(a, b) \\cdot \\operatorname{kgV}(a, b) = a \\cdot b","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">ggT\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">kgV\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{ggT}(a, b) \\cdot \\operatorname{kgV}(a, b) = a \\cdot b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">ggT\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\" style=\"margin-right:0.0139em;\">kgV\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","lower",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Fggt-und-kgv",[],[2266,2267],"fraction-reducing","fraction-addition",{"title":548,"description":2208},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fggt-und-kgv","Der größte gemeinsame Teiler mal das kleinste gemeinsame Vielfache zweier Zahlen ergibt das Produkt der beiden Zahlen.",[2272,2273,2274,2275,2276],"ggt","kgv","teiler","vielfache","primfaktorzerlegung",[2278,2282,2286],{"symbol":2279,"meaning":2280,"symbolHtml":2281},"a, b","natürliche Zahlen ab 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2283,"meaning":2284,"symbolHtml":2285},"\\operatorname{ggT}(a, b)","größter gemeinsamer Teiler von a und b","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">ggT\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{ggT}(a, b)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">ggT\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2287,"meaning":2288,"symbolHtml":2289},"\\operatorname{kgV}(a, b)","kleinstes gemeinsames Vielfaches von a und b","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">kgV\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{kgV}(a, b)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\" style=\"margin-right:0.0139em;\">kgV\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","YHe4cNxmuQ4InvHj3tfY1aauwRNF86Cp9ZcYPTwWCwk",[2292,2295],{"stem":2293,"title":2294,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fbrueche-addieren-und-subtrahieren","Brüche addieren und subtrahieren",{"stem":2296,"title":2297,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fbrueche-kuerzen-und-erweitern","Brüche 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