LCM for 8, 9 and 24

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What's the Least Common Multiple (LCM) of 8, 9 and 24?

Answer

LCM of 8, 9 and 24 is
72

First common multiples: 72, 144, 216, …

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

8 = 23

9 = 32

24 = 23 × 3

Prime8924Highest power
223—2323
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
89972
8910360
8911792
891272
8913936
8914504
8915360
8916144
89171,224
891872
89191,368
8920360
8921504
8922792
89231,656
892472
89251,800
8926936
8927216
8928504
89292,088
8930360
89312,232
8932288
8933792
89341,224
89352,520
893672
89372,664
89381,368

FAQ

What's the Least Common Multiple (LCM) of 8, 9 and 24?

LCM of 8, 9 and 24 is 72

How to find the LCM of 8, 9 and 24 by prime factorization?

Take every prime that appears in 8, 9 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, 9 and 24 two numbers at a time?

Yes. The LCM of 8 and 9 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, 9 and 24?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 8, 72 ÷ 9 and 72 ÷ 24 all come out whole. Any other common multiple of 8, 9 and 24 is a multiple of 72.

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