LCM for 12, 24 and 36

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What's the Least Common Multiple (LCM) of 12, 24 and 36?

Answer

LCM of 12, 24 and 36 is
72

First common multiples: 72, 144, 216, …

72 is divisible by all three: 72 ÷ 12 = 6, 72 ÷ 24 = 3, 72 ÷ 36 = 2 — and 6, 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/12 by 6 and of y/24 by 3 and of z/36 by 2.

12 = 22 × 3

24 = 23 × 3

36 = 22 × 32

Prime122436Highest power
222232223
3333232

LCM = 23 × 32 = 72

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See Also

LCM Table

1st2nd3rdLCM
122124168
122224264
122324552
12242424
122425600
122426312
122427216
122428168
122429696
122430120
122431744
12243296
122433264
122434408
122435840
12243672
122437888
122438456
122439312
122440120
122441984
122442168
1224431,032
122444264
122445360
122446552
1224471,128
12244848
1224491,176
122450600

FAQ

What's the Least Common Multiple (LCM) of 12, 24 and 36?

LCM of 12, 24 and 36 is 72

How to find the LCM of 12, 24 and 36 by prime factorization?

Take every prime that appears in 12, 24 and 36 to the highest power it reaches in any one of them and multiply: 2³ × 3² = 72.

Can you get the LCM of 12, 24 and 36 two numbers at a time?

Yes. The LCM of 12 and 24 is 24, and the LCM of 24 and 36 is 72 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 72 divisible by 12, 24 and 36?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 12, 72 ÷ 24 and 72 ÷ 36 all come out whole. Any other common multiple of 12, 24 and 36 is a multiple of 72.

See Also