LCM for 9, 10 and 12

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What's the Least Common Multiple (LCM) of 9, 10 and 12?

Answer

LCM of 9, 10 and 12 is
180

First common multiples: 180, 360, 540, …

180 is divisible by all three: 180 ÷ 9 = 20, 180 ÷ 10 = 18, 180 ÷ 12 = 15 — and 20, 18 and 15 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 20 and of y/10 by 18 and of z/12 by 15.

9 = 32

10 = 2 × 5

12 = 22 × 3

Prime91012Highest power
2—22222
332—332
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 = 22 × 32 × 5 = 180

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LCM Table

1st2nd3rdLCM
191090
291090
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

FAQ

What's the Least Common Multiple (LCM) of 9, 10 and 12?

LCM of 9, 10 and 12 is 180

How to find the LCM of 9, 10 and 12 by prime factorization?

Take every prime that appears in 9, 10 and 12 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 9, 10 and 12 two numbers at a time?

Yes. The LCM of 9 and 10 is 90, and the LCM of 90 and 12 is 180 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 180 divisible by 9, 10 and 12?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 9, 180 ÷ 10 and 180 ÷ 12 all come out whole. Any other common multiple of 9, 10 and 12 is a multiple of 180.

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