LCM for 5, 6 and 7

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 5, 6 and 7?

Answer

LCM of 5, 6 and 7 is
210

First common multiples: 210, 420, 630, …

210 is divisible by all three: 210 ÷ 5 = 42, 210 ÷ 6 = 35, 210 ÷ 7 = 30 — and 42, 35 and 30 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/5 by 42 and of y/6 by 35 and of z/7 by 30.

5 — prime

6 = 2 × 3

7 — prime

Prime567Highest power
2—2—2
3—3—3
55——5
7——77

— = 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
15630
25630
35630
45660
55630
56630
567210
568120
56990
561030
5611330
561260
5613390
5614210
561530
5616240
5617510
561890
5619570
562060
5621210
5622330
5623690
5624120
5625150
5626390
5627270
5628420
5629870
563030

FAQ

What's the Least Common Multiple (LCM) of 5, 6 and 7?

LCM of 5, 6 and 7 is 210

How to find the LCM of 5, 6 and 7 by prime factorization?

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

Can you get the LCM of 5, 6 and 7 two numbers at a time?

Yes. The LCM of 5 and 6 is 30, and the LCM of 30 and 7 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 5, 6 and 7?

Yes, and by definition it is the smallest positive integer that is: 210 ÷ 5, 210 ÷ 6 and 210 ÷ 7 all come out whole. Any other common multiple of 5, 6 and 7 is a multiple of 210.

See Also