LCM for 12, 24 and 32

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What's the Least Common Multiple (LCM) of 12, 24 and 32?

Answer

LCM of 12, 24 and 32 is
96

First common multiples: 96, 192, 288, …

96 is divisible by all three: 96 ÷ 12 = 8, 96 ÷ 24 = 4, 96 ÷ 32 = 3 — and 8, 4 and 3 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 8 and of y/24 by 4 and of z/32 by 3.

12 = 22 × 3

24 = 23 × 3

32 = 25

Prime122432Highest power
222232525
333—3

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

LCM = 25 × 3 = 96

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LCM Table

1st2nd3rdLCM
121724408
12182472
121924456
122024120
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

FAQ

What's the Least Common Multiple (LCM) of 12, 24 and 32?

LCM of 12, 24 and 32 is 96

How to find the LCM of 12, 24 and 32 by prime factorization?

Take every prime that appears in 12, 24 and 32 to the highest power it reaches in any one of them and multiply: 2⁵ × 3 = 96.

Can you get the LCM of 12, 24 and 32 two numbers at a time?

Yes. The LCM of 12 and 24 is 24, and the LCM of 24 and 32 is 96 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 96 divisible by 12, 24 and 32?

Yes, and by definition it is the smallest positive integer that is: 96 ÷ 12, 96 ÷ 24 and 96 ÷ 32 all come out whole. Any other common multiple of 12, 24 and 32 is a multiple of 96.

See Also