LCM for 6, 7 and 10

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 6, 7 and 10?

Answer

LCM of 6, 7 and 10 is
210

First common multiples: 210, 420, 630, …

210 is divisible by all three: 210 ÷ 6 = 35, 210 ÷ 7 = 30, 210 ÷ 10 = 21 — and 35, 30 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 35 and of y/7 by 30 and of z/10 by 21.

6 = 2 × 3

7 — prime

10 = 2 × 5

Prime6710Highest power
22—22
33——3
5——55
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 = 2 × 3 × 5 × 7 = 210

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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 10?

LCM of 6, 7 and 10 is 210

How to find the LCM of 6, 7 and 10 by prime factorization?

Take every prime that appears in 6, 7 and 10 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5 × 7 = 210.

Can you get the LCM of 6, 7 and 10 two numbers at a time?

Yes. The LCM of 6 and 7 is 42, and the LCM of 42 and 10 is 210 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 210 divisible by 6, 7 and 10?

Yes, and by definition it is the smallest positive integer that is: 210 ÷ 6, 210 ÷ 7 and 210 ÷ 10 all come out whole. Any other common multiple of 6, 7 and 10 is a multiple of 210.

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