LCM for 6, 15 and 40

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What's the Least Common Multiple (LCM) of 6, 15 and 40?

Answer

LCM of 6, 15 and 40 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 6 = 20, 120 ÷ 15 = 8, 120 ÷ 40 = 3 — and 20, 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/6 by 20 and of y/15 by 8 and of z/40 by 3.

6 = 2 × 3

15 = 3 × 5

40 = 23 × 5

Prime61540Highest power
22—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
61525150
61526390
61527270
61528420
61529870
6153030
61531930
61532480
61533330
61534510
61535210
61536180
615371,110
61538570
61539390
61540120
615411,230
61542210
615431,290
61544660
6154590
61546690
615471,410
61548240
615491,470
61550150
61551510
61552780
615531,590
61554270

FAQ

What's the Least Common Multiple (LCM) of 6, 15 and 40?

LCM of 6, 15 and 40 is 120

How to find the LCM of 6, 15 and 40 by prime factorization?

Take every prime that appears in 6, 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 6, 15 and 40 two numbers at a time?

Yes. The LCM of 6 and 15 is 30, and the LCM of 30 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 6, 15 and 40?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 6, 120 ÷ 15 and 120 ÷ 40 all come out whole. Any other common multiple of 6, 15 and 40 is a multiple of 120.

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