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The Least Common Multiple of Every Number From 1 Through 100
The Least Common Multiple of Every Number From 1 Through 100
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The way to find the Least Common multiple of all numbers below a specific limit can be determined with the following steps:
- Determine all prime numbers below the limit.
- The primes below 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
- Find the highest power of each prime that falls below the limit.
-
Note: ∴
is the therefore
symbol.
- Write the resultant equation
- According to the Order of Operations, exponents are calculated first.
- Perform the multiplications, going from left to right.
- I will be using the Lattice method of multiplication, as that will allow me to keep track of what’s going on and, ∴, keep my sanity intact.
6
4
8
4
2
5
4
9
1
1
1
3
1
7
1
9
2
3
2
9
3
1
3
7
4
1
4
3
4
7
5
3
5
9
6
1
6
7
7
1
7
3
7
9
8
3
8
9
9
7
LCM(1...100) ÷ Each Factor ≤ 100
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
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