LCM for 18, 24 and 36

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What's the Least Common Multiple (LCM) of 18, 24 and 36?

Answer

LCM of 18, 24 and 36 is
72

First common multiples: 72, 144, 216, …

72 is divisible by all three: 72 ÷ 18 = 4, 72 ÷ 24 = 3, 72 ÷ 36 = 2 — and 4, 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/18 by 4 and of y/24 by 3 and of z/36 by 2.

18 = 2 × 32

24 = 23 × 3

36 = 22 × 32

Prime182436Highest power
22232223
33233232

LCM = 23 × 32 = 72

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LCM Table

1st2nd3rdLCM
182124504
182224792
1823241,656
18242472
1824251,800
182426936
182427216
182428504
1824292,088
182430360
1824312,232
182432288
182433792
1824341,224
1824352,520
18243672
1824372,664
1824381,368
182439936
182440360
1824412,952
182442504
1824433,096
182444792
182445360
1824461,656
1824473,384
182448144
1824493,528
1824501,800

FAQ

What's the Least Common Multiple (LCM) of 18, 24 and 36?

LCM of 18, 24 and 36 is 72

How to find the LCM of 18, 24 and 36 by prime factorization?

Take every prime that appears in 18, 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 18, 24 and 36 two numbers at a time?

Yes. The LCM of 18 and 24 is 72, and the LCM of 72 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 18, 24 and 36?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 18, 72 ÷ 24 and 72 ÷ 36 all come out whole. Any other common multiple of 18, 24 and 36 is a multiple of 72.

See Also