LCM for 7, 8 and 9

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 7, 8 and 9?

Answer

LCM of 7, 8 and 9 is
504

First common multiples: 504; 1,008; 1,512; …

504 is divisible by all three: 504 ÷ 7 = 72, 504 ÷ 8 = 63, 504 ÷ 9 = 56 — and 72, 63 and 56 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/7 by 72 and of y/8 by 63 and of z/9 by 56.

7 — prime

8 = 23

9 = 32

Prime789Highest power
2—23—23
3——3232
77——7

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

LCM = 23 × 32 × 7 = 504

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LCM Table

1st2nd3rdLCM
17856
27856
378168
47856
578280
678168
77856
78856
789504
7810280
7811616
7812168
7813728
781456
7815840
7816112
7817952
7818504
78191,064
7820280
7821168
7822616
78231,288
7824168
78251,400
7826728
78271,512
782856
78291,624
7830840

FAQ

What's the Least Common Multiple (LCM) of 7, 8 and 9?

LCM of 7, 8 and 9 is 504

How to find the LCM of 7, 8 and 9 by prime factorization?

Take every prime that appears in 7, 8 and 9 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 7 = 504.

Can you get the LCM of 7, 8 and 9 two numbers at a time?

Yes. The LCM of 7 and 8 is 56, and the LCM of 56 and 9 is 504 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 504 divisible by 7, 8 and 9?

Yes, and by definition it is the smallest positive integer that is: 504 ÷ 7, 504 ÷ 8 and 504 ÷ 9 all come out whole. Any other common multiple of 7, 8 and 9 is a multiple of 504.

See Also