LCM for 6, 9 and 12

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What's the Least Common Multiple (LCM) of 6, 9 and 12?

Answer

LCM of 6, 9 and 12 is
36

First common multiples: 36, 72, 108, …

36 is divisible by all three: 36 ÷ 6 = 6, 36 ÷ 9 = 4, 36 ÷ 12 = 3 — and 6, 4 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/6 by 6 and of y/9 by 4 and of z/12 by 3.

6 = 2 × 3

9 = 32

12 = 22 × 3

Prime6912Highest power
22—2222
3332332

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

LCM = 22 × 32 = 36

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LCM Table

1st2nd3rdLCM
16918
26918
36918
46936
56990
66918
679126
68972
69918
691090
6911198
691236
6913234
6914126
691590
6916144
6917306
691818
6919342
6920180
6921126
6922198
6923414
692472
6925450
6926234
692754
6928252
6929522
693090

FAQ

What's the Least Common Multiple (LCM) of 6, 9 and 12?

LCM of 6, 9 and 12 is 36

How to find the LCM of 6, 9 and 12 by prime factorization?

Take every prime that appears in 6, 9 and 12 to the highest power it reaches in any one of them and multiply: 2² × 3² = 36.

Can you get the LCM of 6, 9 and 12 two numbers at a time?

Yes. The LCM of 6 and 9 is 18, and the LCM of 18 and 12 is 36 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 36 divisible by 6, 9 and 12?

Yes, and by definition it is the smallest positive integer that is: 36 ÷ 6, 36 ÷ 9 and 36 ÷ 12 all come out whole. Any other common multiple of 6, 9 and 12 is a multiple of 36.

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