LCM for 8, 18 and 24

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What's the Least Common Multiple (LCM) of 8, 18 and 24?

Answer

LCM of 8, 18 and 24 is
72

First common multiples: 72, 144, 216, …

72 is divisible by all three: 72 ÷ 8 = 9, 72 ÷ 18 = 4, 72 ÷ 24 = 3 — and 9, 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/8 by 9 and of y/18 by 4 and of z/24 by 3.

8 = 23

18 = 2 × 32

24 = 23 × 3

Prime81824Highest power
22322323
3—32332

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

LCM = 23 × 32 = 72

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LCM Table

1st2nd3rdLCM
891872
81018360
81118792
8121872
81318936
81418504
81518360
81618144
817181,224
8181872
818191,368
81820360
81821504
81822792
818231,656
8182472
818251,800
81826936
81827216
81828504
818292,088
81830360
818312,232
81832288
81833792
818341,224
818352,520
8183672
818372,664
818381,368

FAQ

What's the Least Common Multiple (LCM) of 8, 18 and 24?

LCM of 8, 18 and 24 is 72

How to find the LCM of 8, 18 and 24 by prime factorization?

Take every prime that appears in 8, 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 8, 18 and 24 two numbers at a time?

Yes. The LCM of 8 and 18 is 72, and the LCM of 72 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 8, 18 and 24?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 8, 72 ÷ 18 and 72 ÷ 24 all come out whole. Any other common multiple of 8, 18 and 24 is a multiple of 72.

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