LCM for 6, 7 and 12

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What's the Least Common Multiple (LCM) of 6, 7 and 12?

Answer

LCM of 6, 7 and 12 is
84

First common multiples: 84, 168, 252, …

84 is divisible by all three: 84 ÷ 6 = 14, 84 ÷ 7 = 12, 84 ÷ 12 = 7 — and 14, 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/6 by 14 and of y/7 by 12 and of z/12 by 7.

6 = 2 × 3

7 — prime

12 = 22 × 3

Prime6712Highest power
22—2222
33—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
16742
26742
36742
46784
567210
66742
67742
678168
679126
6710210
6711462
671284
6713546
671442
6715210
6716336
6717714
6718126
6719798
6720420
672142
6722462
6723966
6724168
67251,050
6726546
6727378
672884
67291,218
6730210

FAQ

What's the Least Common Multiple (LCM) of 6, 7 and 12?

LCM of 6, 7 and 12 is 84

How to find the LCM of 6, 7 and 12 by prime factorization?

Take every prime that appears in 6, 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 6, 7 and 12 two numbers at a time?

Yes. The LCM of 6 and 7 is 42, and the LCM of 42 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 6, 7 and 12?

Yes, and by definition it is the smallest positive integer that is: 84 ÷ 6, 84 ÷ 7 and 84 ÷ 12 all come out whole. Any other common multiple of 6, 7 and 12 is a multiple of 84.

See Also