LCM for 4, 9 and 10

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What's the Least Common Multiple (LCM) of 4, 9 and 10?

Answer

LCM of 4, 9 and 10 is
180

First common multiples: 180, 360, 540, …

180 is divisible by all three: 180 ÷ 4 = 45, 180 ÷ 9 = 20, 180 ÷ 10 = 18 — and 45, 20 and 18 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 45 and of y/9 by 20 and of z/10 by 18.

4 = 22

9 = 32

10 = 2 × 5

Prime4910Highest power
222—222
3—32—32
5——55

— = 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
14936
24936
34936
44936
459180
46936
479252
48972
49936
4910180
4911396
491236
4913468
4914252
4915180
4916144
4917612
491836
4919684
4920180
4921252
4922396
4923828
492472
4925900
4926468
4927108
4928252
49291,044
4930180

FAQ

What's the Least Common Multiple (LCM) of 4, 9 and 10?

LCM of 4, 9 and 10 is 180

How to find the LCM of 4, 9 and 10 by prime factorization?

Take every prime that appears in 4, 9 and 10 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 4, 9 and 10 two numbers at a time?

Yes. The LCM of 4 and 9 is 36, and the LCM of 36 and 10 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 4, 9 and 10?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 4, 180 ÷ 9 and 180 ÷ 10 all come out whole. Any other common multiple of 4, 9 and 10 is a multiple of 180.

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