LCM for 12, 18 and 24

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What's the Least Common Multiple (LCM) of 12, 18 and 24?

Answer

LCM of 12, 18 and 24 is
72

First common multiples: 72, 144, 216, …

72 is divisible by all three: 72 ÷ 12 = 6, 72 ÷ 18 = 4, 72 ÷ 24 = 3 — and 6, 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 6 and of y/18 by 4 and of z/24 by 3.

12 = 22 × 3

18 = 2 × 32

24 = 23 × 3

Prime121824Highest power
22222323
3332332

LCM = 23 × 32 = 72

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LCM Table

1st2nd3rdLCM
9121836
101218180
111218396
12121836
121318468
121418252
121518180
121618144
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

FAQ

What's the Least Common Multiple (LCM) of 12, 18 and 24?

LCM of 12, 18 and 24 is 72

How to find the LCM of 12, 18 and 24 by prime factorization?

Take every prime that appears in 12, 18 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3² = 72.

Can you get the LCM of 12, 18 and 24 two numbers at a time?

Yes. The LCM of 12 and 18 is 36, and the LCM of 36 and 24 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, 18 and 24?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 12, 72 ÷ 18 and 72 ÷ 24 all come out whole. Any other common multiple of 12, 18 and 24 is a multiple of 72.

See Also