LCM for 4, 7 and 12

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What's the Least Common Multiple (LCM) of 4, 7 and 12?

Answer

LCM of 4, 7 and 12 is
84

First common multiples: 84, 168, 252, …

84 is divisible by all three: 84 ÷ 4 = 21, 84 ÷ 7 = 12, 84 ÷ 12 = 7 — and 21, 12 and 7 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/4 by 21 and of y/7 by 12 and of z/12 by 7.

4 = 22

7 — prime

12 = 22 × 3

Prime4712Highest power
222—2222
3——33
7—7—7

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

LCM = 22 × 3 × 7 = 84

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LCM Table

1st2nd3rdLCM
14728
24728
34784
44728
457140
46784
47728
47856
479252
4710140
4711308
471284
4713364
471428
4715420
4716112
4717476
4718252
4719532
4720140
472184
4722308
4723644
4724168
4725700
4726364
4727756
472828
4729812
4730420

FAQ

What's the Least Common Multiple (LCM) of 4, 7 and 12?

LCM of 4, 7 and 12 is 84

How to find the LCM of 4, 7 and 12 by prime factorization?

Take every prime that appears in 4, 7 and 12 to the highest power it reaches in any one of them and multiply: 2² × 3 × 7 = 84.

Can you get the LCM of 4, 7 and 12 two numbers at a time?

Yes. The LCM of 4 and 7 is 28, and the LCM of 28 and 12 is 84 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 84 divisible by 4, 7 and 12?

Yes, and by definition it is the smallest positive integer that is: 84 ÷ 4, 84 ÷ 7 and 84 ÷ 12 all come out whole. Any other common multiple of 4, 7 and 12 is a multiple of 84.

See Also