LCM for 15, 18 and 30

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What's the Least Common Multiple (LCM) of 15, 18 and 30?

Answer

LCM of 15, 18 and 30 is
90

First common multiples: 90, 180, 270, …

90 is divisible by all three: 90 ÷ 15 = 6, 90 ÷ 18 = 5, 90 ÷ 30 = 3 — and 6, 5 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/15 by 6 and of y/18 by 5 and of z/30 by 3.

15 = 3 × 5

18 = 2 × 32

30 = 2 × 3 × 5

Prime151830Highest power
2—222
3332332
55—55

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

LCM = 2 × 32 × 5 = 90

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LCM Table

1st2nd3rdLCM
15151890
151618720
1517181,530
15181890
1518191,710
151820180
151821630
151822990
1518232,070
151824360
151825450
1518261,170
151827270
1518281,260
1518292,610
15183090
1518312,790
1518321,440
151833990
1518341,530
151835630
151836180
1518373,330
1518381,710
1518391,170
151840360
1518413,690
151842630
1518433,870
1518441,980

FAQ

What's the Least Common Multiple (LCM) of 15, 18 and 30?

LCM of 15, 18 and 30 is 90

How to find the LCM of 15, 18 and 30 by prime factorization?

Take every prime that appears in 15, 18 and 30 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

Can you get the LCM of 15, 18 and 30 two numbers at a time?

Yes. The LCM of 15 and 18 is 90, and the LCM of 90 and 30 is 90 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 90 divisible by 15, 18 and 30?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 15, 90 ÷ 18 and 90 ÷ 30 all come out whole. Any other common multiple of 15, 18 and 30 is a multiple of 90.

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