The Least Common Multiple of Every Number From 1 Through 100

The way to find the Least Common multiple of all numbers below a specific limit can be determined with the following steps:

(64 \times 81) \times 25 \times 49 \times 11 \times 13 \times 17 \times 19 \times 23 \times 29 \times 31 \times 37 \times 41 \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

6 4 8 4

64 \times 81 = 5,184

(5,184 \times 25) \times 49 \times 11 \times 13 \times 17 \times 19 \times 23 \times 29 \times 31 \times 37 \times 41 \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

2 5

5,184 \times 25 = 129,600

(129,600 \times 49) \times 11 \times 13 \times 17 \times 19 \times 23 \times 29 \times 31 \times 37 \times 41 \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

4 9

129,600 \times 49 = 6,350,400

(6,350,400 \times 11) \times 13 \times 17 \times 19 \times 23 \times 29 \times 31 \times 37 \times 41 \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

1 1

6,350,400 \times 11 = 69,854,400

(69,854,400 \times 13) \times 17 \times 19 \times 23 \times 29 \times 31 \times 37 \times 41 \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

1 3

69,854,400 \times 13 = 908,107,200

(908,107,200 \times 17) \times 19 \times 23 \times 29 \times 31 \times 37 \times 41 \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

1 7

908,107,200 \times 17 = 15,437,822,500

(15,437,822,500 \times 19) \times 23 \times 29 \times 31 \times 37 \times 41 \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

1 9

15,437,822,500 \times 19 = 293,318,625,600

(293,318,625,600 \times 23) \times 29 \times 31 \times 37 \times 41 \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

2 3

293,318,625,600 \times 23 = 6,746,328,388,800

(6,746,328,388,800 \times 29) \times 31 \times 37 \times 41 \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

2 9

6,746,328,388,800 \times 29 = 195,643,523,275,200

(195,643,523,275,200 \times 31) \times 37 \times 41 \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

3 1

195,643,523,275,200 \times 31 = 6,064,949,221,531,200

(6,064,949,221,531,200 \times 37) \times 41 \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

3 7

6,064,949,221,531,200 \times 37 = 224,403,121,196,654,400

(224,403,121,196,654,400 \times 41) \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

4 1

224,403,121,196,654,400 \times 41 = 9,200,527,969,062,830,400

(9,200,527,969,062,830,400 \times 43) \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

4 3

9,200,527,969,062,830,400 \times 43 = 395,622,702,669,701,707,200

(395,622,702,669,701,707,200 \times 47) \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

4 7

395,622,702,669,701,707,200 \times 47 = 18,594,267,025,475,980,238,400

(18,594,267,025,475,980,238,400 \times 53) \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

5 3

18,594,267,025,475,980,238,400 \times 53 = 985,496,152,350,226,952,635,200

(985,496,152,350,226,952,635,200 \times 59) \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

5 9

985,496,152,350,226,952,635,200 \times 59 = 58,144,272,988,663,390,205,476,800

(58,144,272,988,663,390,205,476,800 \times 61) \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

6 1

58,144,272,988,663,390,205,476,800 \times 61 = 3,546,800,652,308,466,802,534,084,800

(3,546,800,652,308,466,802,534,084,800 \times 67) \times 71 \times 73 \times 79 \times 83 \times 89 \times 97

6 7

67 \times 3,546,800,652,308,466,802,534,084,800 = 237,635,643,704,667,275,769,783,681,600

(237,635,643,704,667,275,769,783,681,600 \times 71) \times 73 \times 79 \times 83 \times 89 \times 97

7 1

237,635,643,704,667,275,769,783,681,600 \times 71 = 16,872,130,703,031,376,579,654,641,393,600

(16,872,130,703,031,376,579,654,641,393,600 \times 73) \times 79 \times 83 \times 89 \times 97

7 3

16,872,130,703,031,376,579,654,641,393,600 \times 73 = 1,231,665,541,321,290,490,314,788,821,732,800

(1,231,665,541,321,290,490,314,788,821,732,800 \times 79) \times 83 \times 89 \times 97

7 9

1,231,665,541,321,290,490,314,788,821,732,800 \times 79 = 97,301,577,764,381,948,734,868,316,916,891,200

(97,301,577,764,381,948,734,868,316,916,891,200 \times 83) \times 89 \times 97

8 3

97,301,577,764,381,948,734,868,316,916,891,200 \times 83 = 8,076,030,954,443,701,744,994,070,304,101,969,600

(8,076,030,954,443,701,744,994,070,304,101,969,600 \times 89) \times 97

8 9

8,076,030,954,443,701,744,994,070,304,101,969,600 \times 89 = 718,766,754,945,489,455,304,472,257,065,075,294,400

718,766,754,945,489,455,304,472,257,065,075,294,400 \times 97

9 7

718,766,754,945,489,455,304,472,257,065,075,294,400 \times 97 = 69,720,375,229,712,477,164,533,808,935,312,303,556,800

2^{6} \times 3^{4} \times 5^{2} \times 7^{2} \times 11 \times 13 \times 17 \times 19 \times 23 \times 29 \times 31 \times 37 \times 41 \times 43 \times 47 \times 53 \times 59 \times 61 \times 67 \times 71 \times 73 \times 79 \times 83 \times 89 \times 97 = 69,720,375,229,712,477,164,533,808,935,312,303,556,800

LCM(1...100) ÷ Each Factor ≤ 100

$n \div 1 = 69,720,375,229,712,477,164,533,808,935,312,303,556,800$
$n \div 2 = 34,860,187,614,856,238,582,266,904,467,656,151,778,400$
$n \div 3 = 23,240,125,076,570,825,721,511,269,645,104,101,185,600$
$n \div 4 = 17,430,093,807,428,119,291,133,452,233,828,075,889,200$
$n \div 5 = 13,944,075,045,942,495,432,906,761,787,062,460,711,360$
$n \div 6 = 11,620,062,538,285,412,860,755,634,822,552,050,592,800$
$n \div 7 = 9,960,053,604,244,639,594,933,401,276,473,186,222,400$
$n \div 8 = 8,715,046,903,714,059,645,566,726,116,914,037,944,600$
$n \div 9 = 7,746,708,358,856,941,907,170,423,215,034,700,395,200$
$n \div 10 = 6,972,037,522,971,247,716,453,380,893,531,230,355,680$
$n \div 11 = 6,338,215,929,973,861,560,412,164,448,664,754,868,800$
$n \div 12 = 5,810,031,269,142,706,430,377,817,411,276,025,296,400$
$n \div 13 = 5,363,105,786,900,959,781,887,216,071,947,100,273,600$
$n \div 14 = 4,980,026,802,122,319,797,466,700,638,236,593,111,200$
$n \div 15 = 4,648,025,015,314,165,144,302,253,929,020,820,237,120$
$n \div 16 = 4,357,523,451,857,029,822,783,363,058,457,018,972,300$
$n \div 17 = 4,101,198,542,924,263,362,619,635,819,724,253,150,400$
$n \div 18 = 3,873,354,179,428,470,953,585,211,607,517,350,197,600$
$n \div 19 = 3,669,493,433,142,761,956,028,095,207,121,700,187,200$
$n \div 20 = 3,486,018,761,485,623,858,226,690,446,765,615,177,840$
$n \div 21 = 3,320,017,868,081,546,531,644,467,092,157,728,740,800$
$n \div 22 = 3,169,107,964,986,930,780,206,082,224,332,377,434,400$
$n \div 23 = 3,031,320,662,161,412,050,631,904,736,317,926,241,600$
$n \div 24 = 2,905,015,634,571,353,215,188,908,705,638,012,648,200$
$n \div 25 = 2,788,815,009,188,499,086,581,352,357,412,492,142,272$
$n \div 26 = 2,681,552,893,450,479,890,943,608,035,973,550,136,800$
$n \div 27 = 2,582,236,119,618,980,635,723,474,405,011,566,798,400$
$n \div 28 = 2,490,013,401,061,159,898,733,350,319,118,296,555,600$
$n \div 29 = 2,404,150,869,990,085,419,466,683,066,734,907,019,200$
$n \div 30 = 2,324,012,507,657,082,572,151,126,964,510,410,118,560$
$n \div 31 = 2,249,044,362,248,789,585,952,703,514,042,332,372,800$
$n \div 32 = 2,178,761,725,928,514,911,391,681,529,228,509,486,150$
$n \div 33 = 2,112,738,643,324,620,520,137,388,149,554,918,289,600$
$n \div 34 = 2,050,599,271,462,131,681,309,817,909,862,126,575,200$
$n \div 35 = 1,992,010,720,848,927,918,986,680,255,294,637,244,480$
$n \div 36 = 1,936,677,089,714,235,476,792,605,803,758,675,098,800$
$n \div 37 = 1,884,334,465,667,904,788,230,643,484,738,170,366,400$
$n \div 38 = 1,834,746,716,571,380,978,014,047,603,560,850,093,600$
$n \div 39 = 1,787,701,928,966,986,593,962,405,357,315,700,091,200$
$n \div 40 = 1,743,009,380,742,811,929,113,345,223,382,807,588,920$
$n \div 41 = 1,700,496,956,822,255,540,598,385,583,788,104,964,800$
$n \div 42 = 1,660,008,934,040,773,265,822,233,546,078,864,370,400$
$n \div 43 = 1,621,404,075,109,592,492,198,460,672,914,239,617,600$
$n \div 44 = 1,584,553,982,493,465,390,103,041,112,166,188,717,200$
$n \div 45 = 1,549,341,671,771,388,381,434,084,643,006,940,079,040$
$n \div 46 = 1,515,660,331,080,706,025,315,952,368,158,963,120,800$
$n \div 47 = 1,483,412,238,930,052,705,628,378,913,517,283,054,400$
$n \div 48 = 1,452,507,817,285,676,607,594,454,352,819,006,324,100$
$n \div 49 = 1,422,864,800,606,377,084,990,485,896,639,026,603,200$
$n \div 50 = 1,394,407,504,594,249,543,290,676,178,706,246,071,136$

$n \div 51 = 1,367,066,180,974,754,454,206,545,273,241,417,716,800$
$n \div 52 = 1,340,776,446,725,239,945,471,804,017,986,775,068,400$
$n \div 53 = 1,315,478,777,919,103,342,727,052,998,779,477,425,600$
$n \div 54 = 1,291,118,059,809,490,317,861,737,202,505,783,399,200$
$n \div 55 = 1,267,643,185,994,772,312,082,432,889,732,950,973,760$
$n \div 56 = 1,245,006,700,530,579,949,366,675,159,559,148,277,800$
$n \div 57 = 1,223,164,477,714,253,985,342,698,402,373,900,062,400$
$n \div 58 = 1,202,075,434,995,042,709,733,341,533,367,453,509,600$
$n \div 59 = 1,181,701,275,079,872,494,314,132,354,835,801,755,200$
$n \div 60 = 1,162,006,253,828,541,286,075,563,482,255,205,059,280$
$n \div 61 = 1,142,956,970,978,893,068,271,046,048,119,873,828,800$
$n \div 62 = 1,124,522,181,124,394,792,976,351,757,021,166,186,400$
$n \div 63 = 1,106,672,622,693,848,843,881,489,030,719,242,913,600$
$n \div 64 = 1,089,380,862,964,257,455,695,840,764,614,254,743,075$
$n \div 65 = 1,072,621,157,380,191,956,377,443,214,389,420,054,720$
$n \div 66 = 1,056,369,321,662,310,260,068,694,074,777,459,144,800$
$n \div 67 = 1,040,602,615,368,842,942,754,235,954,258,392,590,400$
$n \div 68 = 1,025,299,635,731,065,840,654,908,954,931,063,287,600$
$n \div 69 = 1,010,440,220,720,470,683,543,968,245,439,308,747,200$
$n \div 70 = 996,005,360,424,463,959,493,340,127,647,318,622,240$
$n \div 71 = 981,977,115,911,443,340,345,546,604,722,708,500,800$
$n \div 72 = 968,338,544,857,117,738,396,302,901,879,337,549,400$
$n \div 73 = 955,073,633,283,732,563,897,723,410,072,771,281,600$
$n \div 74 = 942,167,232,833,952,394,115,321,742,369,085,183,200$
$n \div 75 = 929,605,003,062,833,028,860,450,785,804,164,047,424$
$n \div 76 = 917,373,358,285,690,489,007,023,801,780,425,046,800$
$n \div 77 = 905,459,418,567,694,508,630,309,206,952,107,838,400$
$n \div 78 = 893,850,964,483,493,296,981,202,678,657,850,045,600$
$n \div 79 = 882,536,395,312,816,166,639,668,467,535,598,779,200$
$n \div 80 = 871,504,690,371,405,964,556,672,611,691,403,794,460$
$n \div 81 = 860,745,373,206,326,878,574,491,468,337,188,932,800$
$n \div 82 = 850,248,478,411,127,770,299,192,791,894,052,482,400$
$n \div 83 = 840,004,520,839,909,363,428,118,179,943,521,729,600$
$n \div 84 = 830,004,467,020,386,632,911,116,773,039,432,185,200$
$n \div 85 = 820,239,708,584,852,672,523,927,163,944,850,630,080$
$n \div 86 = 810,702,037,554,796,246,099,230,336,457,119,808,800$
$n \div 87 = 801,383,623,330,028,473,155,561,022,244,969,006,400$
$n \div 88 = 792,276,991,246,732,695,051,520,556,083,094,358,600$
$n \div 89 = 783,375,002,581,039,069,264,424,819,497,891,051,200$
$n \div 90 = 774,670,835,885,694,190,717,042,321,503,470,039,520$
$n \div 91 = 766,157,969,557,279,968,841,030,867,421,014,324,800$
$n \div 92 = 757,830,165,540,353,012,657,976,184,079,481,560,400$
$n \div 93 = 749,681,454,082,929,861,984,234,504,680,777,457,600$
$n \div 94 = 741,706,119,465,026,352,814,189,456,758,641,527,200$
$n \div 95 = 733,898,686,628,552,391,205,619,041,424,340,037,440$
$n \div 96 = 726,253,908,642,838,303,797,227,176,409,503,162,050$
$n \div 97 = 718,766,754,945,489,455,304,472,257,065,075,294,400$
$n \div 98 = 711,432,400,303,188,542,495,242,948,319,513,301,600$
$n \div 99 = 704,246,214,441,540,173,379,129,383,184,972,763,200$
$n \div 100 = 697,203,752,297,124,771,645,338,089,353,123,035,568$

Prime Factorization Tree

69,720,375,229,712,477,164,533,808,935,312,303,556,800 2 3 5 7 34,860,187,614,856,238,582,266,904,467,656,151,778,400 17,430,093,807,428,119,291,133,452,233,828,075,889,200 8,715,046,903,714,059,645,566,726,116,914,037,944,600 4,357,523,451,857,029,822,783,363,058,457,018,972,300 2,178,761,725,928,514,911,391,681,529,228,509,486,150 1,089,380,862,964,257,455,695,840,764,614,254,743,075 363,126,954,321,419,151,898,613,588,204,751,581,025 121,042,318,107,139,717,299,537,862,734,917,193,675 40,347,439,369,046,572,433,179,287,578,305,731,225 13,449,146,456,348,857,477,726,429,192,768,577,075 2,689,829,291,269,771,495,545,285,838,553,715,415 537,965,858,253,954,299,109,057,167,710,743,083 76,852,265,464,850,614,158,436,738,244,391,869 10,978,895,066,407,230,594,062,391,177,770,267 11 998,081,369,673,384,599,460,217,379,797,297 13 76,775,489,974,875,738,420,016,721,522,869 17 4,516,205,292,639,749,318,824,513,030,757 19 237,695,015,402,092,069,411,816,475,303 23 10,334,565,887,047,481,278,774,629,361 29 356,364,340,932,671,768,233,607,909 31 11,495,623,901,053,928,007,535,739 37 310,692,537,866,322,378,582,047 41 7,577,866,777,227,375,087,367 43 176,229,459,935,520,350,869 47 3,749,562,977,351,496,827 53 70,746,471,270,782,959 59 1,199,092,733,403,101 61 19,657,257,924,641 67 293,391,909,323 71 4,132,280,413 73 56,606,581 79 716,539 83 8,633 89 97