LCM for 6, 8 and 12

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What's the Least Common Multiple (LCM) of 6, 8 and 12?

Answer

LCM of 6, 8 and 12 is
24

First common multiples: 24, 48, 72, …

24 is divisible by all three: 24 ÷ 6 = 4, 24 ÷ 8 = 3, 24 ÷ 12 = 2 — and 4, 3 and 2 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 4 and of y/8 by 3 and of z/12 by 2.

6 = 2 × 3

8 = 23

12 = 22 × 3

Prime6812Highest power
22232223
33—33

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

LCM = 23 × 3 = 24

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LCM Table

1st2nd3rdLCM
16824
26824
36824
46824
568120
66824
678168
68824
68972
6810120
6811264
681224
6813312
6814168
6815120
681648
6817408
681872
6819456
6820120
6821168
6822264
6823552
682424
6825600
6826312
6827216
6828168
6829696
6830120

FAQ

What's the Least Common Multiple (LCM) of 6, 8 and 12?

LCM of 6, 8 and 12 is 24

How to find the LCM of 6, 8 and 12 by prime factorization?

Take every prime that appears in 6, 8 and 12 to the highest power it reaches in any one of them and multiply: 2³ × 3 = 24.

Can you get the LCM of 6, 8 and 12 two numbers at a time?

Yes. The LCM of 6 and 8 is 24, and the LCM of 24 and 12 is 24 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 24 divisible by 6, 8 and 12?

Yes, and by definition it is the smallest positive integer that is: 24 ÷ 6, 24 ÷ 8 and 24 ÷ 12 all come out whole. Any other common multiple of 6, 8 and 12 is a multiple of 24.

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