LCM for 4, 5 and 15

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What's the Least Common Multiple (LCM) of 4, 5 and 15?

Answer

LCM of 4, 5 and 15 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 4 = 15, 60 ÷ 5 = 12, 60 ÷ 15 = 4 — and 15, 12 and 4 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/4 by 15 and of y/5 by 12 and of z/15 by 4.

4 = 22

5 — prime

15 = 3 × 5

Prime4515Highest power
222——22
3——33
5—555

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

LCM = 22 × 3 × 5 = 60

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LCM Table

1st2nd3rdLCM
14520
24520
34560
44520
45520
45660
457140
45840
459180
451020
4511220
451260
4513260
4514140
451560
451680
4517340
4518180
4519380
452020
4521420
4522220
4523460
4524120
4525100
4526260
4527540
4528140
4529580
453060

FAQ

What's the Least Common Multiple (LCM) of 4, 5 and 15?

LCM of 4, 5 and 15 is 60

How to find the LCM of 4, 5 and 15 by prime factorization?

Take every prime that appears in 4, 5 and 15 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 4, 5 and 15 two numbers at a time?

Yes. The LCM of 4 and 5 is 20, and the LCM of 20 and 15 is 60 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 60 divisible by 4, 5 and 15?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 4, 60 ÷ 5 and 60 ÷ 15 all come out whole. Any other common multiple of 4, 5 and 15 is a multiple of 60.

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