LCM for 8, 10 and 12

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What's the Least Common Multiple (LCM) of 8, 10 and 12?

Answer

LCM of 8, 10 and 12 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 8 = 15, 120 ÷ 10 = 12, 120 ÷ 12 = 10 — and 15, 12 and 10 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 15 and of y/10 by 12 and of z/12 by 10.

8 = 23

10 = 2 × 5

12 = 22 × 3

Prime81012Highest power
22322223
3——33
5—5—5

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

LCM = 23 × 3 × 5 = 120

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LCM Table

1st2nd3rdLCM
181040
281040
3810120
481040
581040
6810120
7810280
881040
8910360
8101040
81011440
81012120
81013520
81014280
81015120
8101680
81017680
81018360
81019760
8102040
81021840
81022440
81023920
81024120
81025200
81026520
810271,080
81028280
810291,160
81030120

FAQ

What's the Least Common Multiple (LCM) of 8, 10 and 12?

LCM of 8, 10 and 12 is 120

How to find the LCM of 8, 10 and 12 by prime factorization?

Take every prime that appears in 8, 10 and 12 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 8, 10 and 12 two numbers at a time?

Yes. The LCM of 8 and 10 is 40, and the LCM of 40 and 12 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 8, 10 and 12?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 8, 120 ÷ 10 and 120 ÷ 12 all come out whole. Any other common multiple of 8, 10 and 12 is a multiple of 120.

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