LCM for 8, 9 and 10

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What's the Least Common Multiple (LCM) of 8, 9 and 10?

Answer

LCM of 8, 9 and 10 is
360

First common multiples: 360; 720; 1,080; …

360 is divisible by all three: 360 ÷ 8 = 45, 360 ÷ 9 = 40, 360 ÷ 10 = 36 — and 45, 40 and 36 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 45 and of y/9 by 40 and of z/10 by 36.

8 = 23

9 = 32

10 = 2 × 5

Prime8910Highest power
223—223
3—32—32
5——55

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

LCM = 23 × 32 × 5 = 360

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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 10?

LCM of 8, 9 and 10 is 360

How to find the LCM of 8, 9 and 10 by prime factorization?

Take every prime that appears in 8, 9 and 10 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

Can you get the LCM of 8, 9 and 10 two numbers at a time?

Yes. The LCM of 8 and 9 is 72, and the LCM of 72 and 10 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 360 divisible by 8, 9 and 10?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 8, 360 ÷ 9 and 360 ÷ 10 all come out whole. Any other common multiple of 8, 9 and 10 is a multiple of 360.

See Also