LCM for 21 and 100

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What's the Least Common Multiple (LCM) of 21 and 100?

Answer

LCM of 21 and 100 is
2,100

First common multiples: 2,100; 4,200; 6,300; …

2,100 is divisible by both: 2,100 ÷ 21 = 100; 2,100 ÷ 100 = 21 — and 100 and 21 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/21 by 100 and of y/100 by 21.

21 and 100 are coprime (GCF = 1), so their LCM is simply the product: 21 × 100 = 2,100.

21 = 3 × 7

100 = 22 × 52

Prime21100Highest power
2—2222
33—3
5—5252
77—7

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 22 × 3 × 52 × 7 = 2,100

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LCM Table

Number 1Number 2LCM
2129609
2130210
2132672
2133231
2134714
2135105
2136252
2139273
2140840
2141861
214242
2143903
2144924
2145315
2146966
2147987
2148336
2149147
2151357
21521,092
21531,113
2156168
21581,218
21591,239
2160420
2169483
21801,680
218484
211002,100
21105105

FAQ

What's the Least Common Multiple (LCM) of 21 and 100?

LCM of 21 and 100 is 2,100

How to find the LCM of 21 and 100 using prime factorization?

To find the LCM of 21 and 100, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 2,100.

What is the difference between LCM and GCF?

LCM (Least Common Multiple) is the smallest number divisible by both numbers, while GCF (Greatest Common Factor) is the largest number that divides both. For 21 and 100: LCM = 2,100, GCF = 1.

See Also