LCM for 12, 15 and 40

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What's the Least Common Multiple (LCM) of 12, 15 and 40?

Answer

LCM of 12, 15 and 40 is
120

First common multiples: 120, 240, 360, …

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

12 = 22 × 3

15 = 3 × 5

40 = 23 × 5

Prime121540Highest power
222—2323
333—3
5—555

— = 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
121525300
121526780
121527540
121528420
1215291,740
12153060
1215311,860
121532480
121533660
1215341,020
121535420
121536180
1215372,220
1215381,140
121539780
121540120
1215412,460
121542420
1215432,580
121544660
121545180
1215461,380
1215472,820
121548240
1215492,940
121550300
1215511,020
121552780
1215533,180
121554540

FAQ

What's the Least Common Multiple (LCM) of 12, 15 and 40?

LCM of 12, 15 and 40 is 120

How to find the LCM of 12, 15 and 40 by prime factorization?

Take every prime that appears in 12, 15 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 12, 15 and 40 two numbers at a time?

Yes. The LCM of 12 and 15 is 60, and the LCM of 60 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 12, 15 and 40?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 12, 120 ÷ 15 and 120 ÷ 40 all come out whole. Any other common multiple of 12, 15 and 40 is a multiple of 120.

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