LCM for 5, 10 and 15

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What's the Least Common Multiple (LCM) of 5, 10 and 15?

Answer

LCM of 5, 10 and 15 is
30

First common multiples: 30, 60, 90, …

30 is divisible by all three: 30 ÷ 5 = 6, 30 ÷ 10 = 3, 30 ÷ 15 = 2 — and 6, 3 and 2 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/5 by 6 and of y/10 by 3 and of z/15 by 2.

5 — prime

10 = 2 × 5

15 = 3 × 5

Prime51015Highest power
2—2—2
3——33
55555

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

LCM = 2 × 3 × 5 = 30

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LCM Table

1st2nd3rdLCM
151010
251010
351030
451020
551010
561030
571070
581040
591090
5101010
51011110
5101260
51013130
5101470
5101530
5101680
51017170
5101890
51019190
5102020
51021210
51022110
51023230
51024120
5102550
51026130
51027270
51028140
51029290
5103030

FAQ

What's the Least Common Multiple (LCM) of 5, 10 and 15?

LCM of 5, 10 and 15 is 30

How to find the LCM of 5, 10 and 15 by prime factorization?

Take every prime that appears in 5, 10 and 15 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5 = 30.

Can you get the LCM of 5, 10 and 15 two numbers at a time?

Yes. The LCM of 5 and 10 is 10, and the LCM of 10 and 15 is 30 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 30 divisible by 5, 10 and 15?

Yes, and by definition it is the smallest positive integer that is: 30 ÷ 5, 30 ÷ 10 and 30 ÷ 15 all come out whole. Any other common multiple of 5, 10 and 15 is a multiple of 30.

See Also