LCM for 3, 8 and 12

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 3, 8 and 12?

Answer

LCM of 3, 8 and 12 is
24

First common multiples: 24, 48, 72, …

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

3 — prime

8 = 23

12 = 22 × 3

Prime3812Highest power
2—232223
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
13824
23824
33824
34824
358120
36824
378168
38824
38972
3810120
3811264
381224
3813312
3814168
3815120
381648
3817408
381872
3819456
3820120
3821168
3822264
3823552
382424
3825600
3826312
3827216
3828168
3829696
3830120

FAQ

What's the Least Common Multiple (LCM) of 3, 8 and 12?

LCM of 3, 8 and 12 is 24

How to find the LCM of 3, 8 and 12 by prime factorization?

Take every prime that appears in 3, 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 3, 8 and 12 two numbers at a time?

Yes. The LCM of 3 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 3, 8 and 12?

Yes, and by definition it is the smallest positive integer that is: 24 ÷ 3, 24 ÷ 8 and 24 ÷ 12 all come out whole. Any other common multiple of 3, 8 and 12 is a multiple of 24.

See Also