LCM for 6, 7 and 8

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What's the Least Common Multiple (LCM) of 6, 7 and 8?

Answer

LCM of 6, 7 and 8 is
168

First common multiples: 168, 336, 504, …

168 is divisible by all three: 168 ÷ 6 = 28, 168 ÷ 7 = 24, 168 ÷ 8 = 21 — and 28, 24 and 21 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 28 and of y/7 by 24 and of z/8 by 21.

6 = 2 × 3

7 — prime

8 = 23

Prime678Highest power
22—2323
33——3
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 = 23 × 3 × 7 = 168

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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 8?

LCM of 6, 7 and 8 is 168

How to find the LCM of 6, 7 and 8 by prime factorization?

Take every prime that appears in 6, 7 and 8 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 6, 7 and 8 two numbers at a time?

Yes. The LCM of 6 and 7 is 42, and the LCM of 42 and 8 is 168 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 168 divisible by 6, 7 and 8?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 6, 168 ÷ 7 and 168 ÷ 8 all come out whole. Any other common multiple of 6, 7 and 8 is a multiple of 168.

See Also