LCM for 12, 16 and 32

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What's the Least Common Multiple (LCM) of 12, 16 and 32?

Answer

LCM of 12, 16 and 32 is
96

First common multiples: 96, 192, 288, …

96 is divisible by all three: 96 ÷ 12 = 8, 96 ÷ 16 = 6, 96 ÷ 32 = 3 — and 8, 6 and 3 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/12 by 8 and of y/16 by 6 and of z/32 by 3.

12 = 22 × 3

16 = 24

32 = 25

Prime121632Highest power
222242525
33——3

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

LCM = 25 × 3 = 96

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LCM Table

1st2nd3rdLCM
121617816
121618144
121619912
121620240
121621336
121622528
1216231,104
12162448
1216251,200
121626624
121627432
121628336
1216291,392
121630240
1216311,488
12163296
121633528
121634816
1216351,680
121636144
1216371,776
121638912
121639624
121640240
1216411,968
121642336
1216432,064
121644528
121645720
1216461,104

FAQ

What's the Least Common Multiple (LCM) of 12, 16 and 32?

LCM of 12, 16 and 32 is 96

How to find the LCM of 12, 16 and 32 by prime factorization?

Take every prime that appears in 12, 16 and 32 to the highest power it reaches in any one of them and multiply: 2⁵ × 3 = 96.

Can you get the LCM of 12, 16 and 32 two numbers at a time?

Yes. The LCM of 12 and 16 is 48, and the LCM of 48 and 32 is 96 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 96 divisible by 12, 16 and 32?

Yes, and by definition it is the smallest positive integer that is: 96 ÷ 12, 96 ÷ 16 and 96 ÷ 32 all come out whole. Any other common multiple of 12, 16 and 32 is a multiple of 96.

See Also