LCM for 8, 12 and 40

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What's the Least Common Multiple (LCM) of 8, 12 and 40?

Answer

LCM of 8, 12 and 40 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 8 = 15, 120 ÷ 12 = 10, 120 ÷ 40 = 3 — and 15, 10 and 3 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/12 by 10 and of z/40 by 3.

8 = 23

12 = 22 × 3

40 = 23 × 5

Prime81240Highest power
223222323
3—3—3
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 × 3 × 5 = 120

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LCM Table

1st2nd3rdLCM
81225600
81226312
81227216
81228168
81229696
81230120
81231744
8123296
81233264
81234408
81235840
8123672
81237888
81238456
81239312
81240120
81241984
81242168
812431,032
81244264
81245360
81246552
812471,128
8124848
812491,176
81250600
81251408
81252312
812531,272
81254216

FAQ

What's the Least Common Multiple (LCM) of 8, 12 and 40?

LCM of 8, 12 and 40 is 120

How to find the LCM of 8, 12 and 40 by prime factorization?

Take every prime that appears in 8, 12 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 8, 12 and 40 two numbers at a time?

Yes. The LCM of 8 and 12 is 24, and the LCM of 24 and 40 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, 12 and 40?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 8, 120 ÷ 12 and 120 ÷ 40 all come out whole. Any other common multiple of 8, 12 and 40 is a multiple of 120.

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