LCM for 5, 6 and 12

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What's the Least Common Multiple (LCM) of 5, 6 and 12?

Answer

LCM of 5, 6 and 12 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 5 = 12, 60 ÷ 6 = 10, 60 ÷ 12 = 5 — and 12, 10 and 5 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 12 and of y/6 by 10 and of z/12 by 5.

5 — prime

6 = 2 × 3

12 = 22 × 3

Prime5612Highest power
2—22222
3—333
55——5

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

LCM = 22 × 3 × 5 = 60

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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 12?

LCM of 5, 6 and 12 is 60

How to find the LCM of 5, 6 and 12 by prime factorization?

Take every prime that appears in 5, 6 and 12 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 5, 6 and 12 two numbers at a time?

Yes. The LCM of 5 and 6 is 30, and the LCM of 30 and 12 is 60 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 60 divisible by 5, 6 and 12?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 5, 60 ÷ 6 and 60 ÷ 12 all come out whole. Any other common multiple of 5, 6 and 12 is a multiple of 60.

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