LCM for 3, 10 and 18

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 3, 10 and 18?

Answer

LCM of 3, 10 and 18 is
90

First common multiples: 90, 180, 270, …

90 is divisible by all three: 90 ÷ 3 = 30, 90 ÷ 10 = 9, 90 ÷ 18 = 5 — and 30, 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/3 by 30 and of y/10 by 9 and of z/18 by 5.

3 — prime

10 = 2 × 5

18 = 2 × 32

Prime31018Highest power
2—222
33—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
331030
341060
351030
361030
3710210
3810120
391090
3101030
31011330
3101260
31013390
31014210
3101530
31016240
31017510
3101890
31019570
3102060
31021210
31022330
31023690
31024120
31025150
31026390
31027270
31028420
31029870
3103030
31031930
31032480

FAQ

What's the Least Common Multiple (LCM) of 3, 10 and 18?

LCM of 3, 10 and 18 is 90

How to find the LCM of 3, 10 and 18 by prime factorization?

Take every prime that appears in 3, 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 3, 10 and 18 two numbers at a time?

Yes. The LCM of 3 and 10 is 30, and the LCM of 30 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 3, 10 and 18?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 3, 90 ÷ 10 and 90 ÷ 18 all come out whole. Any other common multiple of 3, 10 and 18 is a multiple of 90.

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