LCM for 12, 16 and 18

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 12, 16 and 18?

Answer

LCM of 12, 16 and 18 is
144

First common multiples: 144, 288, 432, …

144 is divisible by all three: 144 ÷ 12 = 12, 144 ÷ 16 = 9, 144 ÷ 18 = 8 — and 12, 9 and 8 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 12 and of y/16 by 9 and of z/18 by 8.

12 = 22 × 3

16 = 24

18 = 2 × 32

Prime121618Highest power
22224224
33—3232

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

LCM = 24 × 32 = 144

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LCM Table

1st2nd3rdLCM
3121648
4121648
51216240
6121648
71216336
8121648
91216144
101216240
111216528
12121648
121316624
121416336
121516240
12161648
121617816
121618144
121619912
121620240
121621336
121622528
1216231,104
12162448
1216251,200
121626624
121627432
121628336
1216291,392
121630240
1216311,488
12163296

FAQ

What's the Least Common Multiple (LCM) of 12, 16 and 18?

LCM of 12, 16 and 18 is 144

How to find the LCM of 12, 16 and 18 by prime factorization?

Take every prime that appears in 12, 16 and 18 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

Can you get the LCM of 12, 16 and 18 two numbers at a time?

Yes. The LCM of 12 and 16 is 48, and the LCM of 48 and 18 is 144 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 144 divisible by 12, 16 and 18?

Yes, and by definition it is the smallest positive integer that is: 144 ÷ 12, 144 ÷ 16 and 144 ÷ 18 all come out whole. Any other common multiple of 12, 16 and 18 is a multiple of 144.

See Also