LCM for 6, 8 and 9

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What's the Least Common Multiple (LCM) of 6, 8 and 9?

Answer

LCM of 6, 8 and 9 is
72

First common multiples: 72, 144, 216, …

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

6 = 2 × 3

8 = 23

9 = 32

Prime689Highest power
2223—23
33—3232

— = 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
16824
26824
36824
46824
568120
66824
678168
68824
68972
6810120
6811264
681224
6813312
6814168
6815120
681648
6817408
681872
6819456
6820120
6821168
6822264
6823552
682424
6825600
6826312
6827216
6828168
6829696
6830120

FAQ

What's the Least Common Multiple (LCM) of 6, 8 and 9?

LCM of 6, 8 and 9 is 72

How to find the LCM of 6, 8 and 9 by prime factorization?

Take every prime that appears in 6, 8 and 9 to the highest power it reaches in any one of them and multiply: 2³ × 3² = 72.

Can you get the LCM of 6, 8 and 9 two numbers at a time?

Yes. The LCM of 6 and 8 is 24, and the LCM of 24 and 9 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 6, 8 and 9?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 6, 72 ÷ 8 and 72 ÷ 9 all come out whole. Any other common multiple of 6, 8 and 9 is a multiple of 72.

See Also