LCM for 8, 9 and 12

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What's the Least Common Multiple (LCM) of 8, 9 and 12?

Answer

LCM of 8, 9 and 12 is
72

First common multiples: 72, 144, 216, …

72 is divisible by all three: 72 ÷ 8 = 9, 72 ÷ 9 = 8, 72 ÷ 12 = 6 — and 9, 8 and 6 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/12 by 6.

8 = 23

9 = 32

12 = 22 × 3

Prime8912Highest power
223—2223
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
18972
28972
38972
48972
589360
68972
789504
88972
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

FAQ

What's the Least Common Multiple (LCM) of 8, 9 and 12?

LCM of 8, 9 and 12 is 72

How to find the LCM of 8, 9 and 12 by prime factorization?

Take every prime that appears in 8, 9 and 12 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 12 two numbers at a time?

Yes. The LCM of 8 and 9 is 72, and the LCM of 72 and 12 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 12?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 8, 72 ÷ 9 and 72 ÷ 12 all come out whole. Any other common multiple of 8, 9 and 12 is a multiple of 72.

See Also