LCM for 6, 10 and 12

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What's the Least Common Multiple (LCM) of 6, 10 and 12?

Answer

LCM of 6, 10 and 12 is
60

First common multiples: 60, 120, 180, …

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

6 = 2 × 3

10 = 2 × 5

12 = 22 × 3

Prime61012Highest power
2222222
33—33
5—5—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
161030
261030
361030
461060
561030
661030
6710210
6810120
691090
6101030
61011330
6101260
61013390
61014210
6101530
61016240
61017510
6101890
61019570
6102060
61021210
61022330
61023690
61024120
61025150
61026390
61027270
61028420
61029870
6103030

FAQ

What's the Least Common Multiple (LCM) of 6, 10 and 12?

LCM of 6, 10 and 12 is 60

How to find the LCM of 6, 10 and 12 by prime factorization?

Take every prime that appears in 6, 10 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 6, 10 and 12 two numbers at a time?

Yes. The LCM of 6 and 10 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 6, 10 and 12?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 6, 60 ÷ 10 and 60 ÷ 12 all come out whole. Any other common multiple of 6, 10 and 12 is a multiple of 60.

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