LCM for 21 and 32

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What's the Least Common Multiple (LCM) of 21 and 32?

Answer

LCM of 21 and 32 is
672

First common multiples: 672; 1,344; 2,016; …

672 is divisible by both: 672 ÷ 21 = 32, 672 ÷ 32 = 21 — and 32 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 32 and of y/32 by 21.

21 and 32 are coprime (GCF = 1), so their LCM is simply the product: 21 × 32 = 672.

21 = 3 × 7

32 = 25

Prime2132Highest power
2—2525
33—3
77—7

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

LCM = 25 × 3 × 7 = 672

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LCM Table

Number 1Number 2LCM
2115105
2122462
2123483
2124168
2125525
2126546
212884
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

FAQ

What's the Least Common Multiple (LCM) of 21 and 32?

LCM of 21 and 32 is 672

How to find the LCM of 21 and 32 using prime factorization?

To find the LCM of 21 and 32, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 672.

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 32: LCM = 672, GCF = 1.

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