LCM for 12, 16 and 20

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 12, 16 and 20?

Answer

LCM of 12, 16 and 20 is
240

First common multiples: 240, 480, 720, …

240 is divisible by all three: 240 ÷ 12 = 20, 240 ÷ 16 = 15, 240 ÷ 20 = 12 — and 20, 15 and 12 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 20 and of y/16 by 15 and of z/20 by 12.

12 = 22 × 3

16 = 24

20 = 22 × 5

Prime121620Highest power
222242224
33——3
5——55

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

LCM = 24 × 3 × 5 = 240

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LCM Table

1st2nd3rdLCM
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
121633528
121634816

FAQ

What's the Least Common Multiple (LCM) of 12, 16 and 20?

LCM of 12, 16 and 20 is 240

How to find the LCM of 12, 16 and 20 by prime factorization?

Take every prime that appears in 12, 16 and 20 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 5 = 240.

Can you get the LCM of 12, 16 and 20 two numbers at a time?

Yes. The LCM of 12 and 16 is 48, and the LCM of 48 and 20 is 240 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 240 divisible by 12, 16 and 20?

Yes, and by definition it is the smallest positive integer that is: 240 ÷ 12, 240 ÷ 16 and 240 ÷ 20 all come out whole. Any other common multiple of 12, 16 and 20 is a multiple of 240.

See Also