LCM for 9, 10 and 18

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What's the Least Common Multiple (LCM) of 9, 10 and 18?

Answer

LCM of 9, 10 and 18 is
90

First common multiples: 90, 180, 270, …

90 is divisible by all three: 90 ÷ 9 = 10, 90 ÷ 10 = 9, 90 ÷ 18 = 5 — and 10, 9 and 5 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/9 by 10 and of y/10 by 9 and of z/18 by 5.

9 = 32

10 = 2 × 5

18 = 2 × 32

Prime91018Highest power
2—222
332—3232
5—5—5

— = 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
391090
4910180
591090
691090
7910630
8910360
991090
9101090
91011990
91012180
910131,170
91014630
9101590
91016720
910171,530
9101890
910191,710
91020180
91021630
91022990
910232,070
91024360
91025450
910261,170
91027270
910281,260
910292,610
9103090
910312,790
910321,440

FAQ

What's the Least Common Multiple (LCM) of 9, 10 and 18?

LCM of 9, 10 and 18 is 90

How to find the LCM of 9, 10 and 18 by prime factorization?

Take every prime that appears in 9, 10 and 18 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

Can you get the LCM of 9, 10 and 18 two numbers at a time?

Yes. The LCM of 9 and 10 is 90, and the LCM of 90 and 18 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 9, 10 and 18?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 9, 90 ÷ 10 and 90 ÷ 18 all come out whole. Any other common multiple of 9, 10 and 18 is a multiple of 90.

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