LCM for 12, 18 and 32

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What's the Least Common Multiple (LCM) of 12, 18 and 32?

Answer

LCM of 12, 18 and 32 is
288

First common multiples: 288, 576, 864, …

288 is divisible by all three: 288 ÷ 12 = 24, 288 ÷ 18 = 16, 288 ÷ 32 = 9 — and 24, 16 and 9 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 24 and of y/18 by 16 and of z/32 by 9.

12 = 22 × 3

18 = 2 × 32

32 = 25

Prime121832Highest power
22222525
3332—32

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

LCM = 25 × 32 = 288

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LCM Table

1st2nd3rdLCM
121718612
12181836
121819684
121820180
121821252
121822396
121823828
12182472
121825900
121826468
121827108
121828252
1218291,044
121830180
1218311,116
121832288
121833396
121834612
1218351,260
12183636
1218371,332
121838684
121839468
121840360
1218411,476
121842252
1218431,548
121844396
121845180
121846828

FAQ

What's the Least Common Multiple (LCM) of 12, 18 and 32?

LCM of 12, 18 and 32 is 288

How to find the LCM of 12, 18 and 32 by prime factorization?

Take every prime that appears in 12, 18 and 32 to the highest power it reaches in any one of them and multiply: 2⁵ × 3² = 288.

Can you get the LCM of 12, 18 and 32 two numbers at a time?

Yes. The LCM of 12 and 18 is 36, and the LCM of 36 and 32 is 288 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 288 divisible by 12, 18 and 32?

Yes, and by definition it is the smallest positive integer that is: 288 ÷ 12, 288 ÷ 18 and 288 ÷ 32 all come out whole. Any other common multiple of 12, 18 and 32 is a multiple of 288.

See Also