LCM for 5, 9 and 10

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What's the Least Common Multiple (LCM) of 5, 9 and 10?

Answer

LCM of 5, 9 and 10 is
90

First common multiples: 90, 180, 270, …

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

5 — prime

9 = 32

10 = 2 × 5

Prime5910Highest power
2——22
3—32—32
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
15945
25990
35945
459180
55945
56990
579315
589360
59945
591090
5911495
5912180
5913585
5914630
591545
5916720
5917765
591890
5919855
5920180
5921315
5922990
59231,035
5924360
5925225
59261,170
5927135
59281,260
59291,305
593090

FAQ

What's the Least Common Multiple (LCM) of 5, 9 and 10?

LCM of 5, 9 and 10 is 90

How to find the LCM of 5, 9 and 10 by prime factorization?

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

Can you get the LCM of 5, 9 and 10 two numbers at a time?

Yes. The LCM of 5 and 9 is 45, and the LCM of 45 and 10 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 5, 9 and 10?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 5, 90 ÷ 9 and 90 ÷ 10 all come out whole. Any other common multiple of 5, 9 and 10 is a multiple of 90.

See Also