LCM for 3, 4 and 12

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 3, 4 and 12?

Answer

LCM of 3, 4 and 12 is
12

First common multiples: 12, 24, 36, …

12 is divisible by all three: 12 ÷ 3 = 4, 12 ÷ 4 = 3, 12 ÷ 12 = 1 — and 4, 3 and 1 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/3 by 4 and of y/4 by 3.

3 — prime

4 = 22

12 = 22 × 3

Prime3412Highest power
2—222222
33—33

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

LCM = 22 × 3 = 12

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LCM Table

1st2nd3rdLCM
13412
23412
33412
34412
34560
34612
34784
34824
34936
341060
3411132
341212
3413156
341484
341560
341648
3417204
341836
3419228
342060
342184
3422132
3423276
342424
3425300
3426156
3427108
342884
3429348
343060

FAQ

What's the Least Common Multiple (LCM) of 3, 4 and 12?

LCM of 3, 4 and 12 is 12

How to find the LCM of 3, 4 and 12 by prime factorization?

Take every prime that appears in 3, 4 and 12 to the highest power it reaches in any one of them and multiply: 2² × 3 = 12.

Can you get the LCM of 3, 4 and 12 two numbers at a time?

Yes. The LCM of 3 and 4 is 12, and the LCM of 12 and 12 is 12 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 12 divisible by 3, 4 and 12?

Yes, and by definition it is the smallest positive integer that is: 12 ÷ 3, 12 ÷ 4 and 12 ÷ 12 all come out whole. Any other common multiple of 3, 4 and 12 is a multiple of 12.

See Also