LCM for 3, 5 and 10

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What's the Least Common Multiple (LCM) of 3, 5 and 10?

Answer

LCM of 3, 5 and 10 is
30

First common multiples: 30, 60, 90, …

30 is divisible by all three: 30 ÷ 3 = 10, 30 ÷ 5 = 6, 30 ÷ 10 = 3 — and 10, 6 and 3 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 10 and of y/5 by 6 and of z/10 by 3.

3 — prime

5 — prime

10 = 2 × 5

Prime3510Highest power
2——22
33——3
5—555

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 2 × 3 × 5 = 30

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LCM Table

1st2nd3rdLCM
13515
23530
33515
34560
35515
35630
357105
358120
35945
351030
3511165
351260
3513195
3514210
351515
3516240
3517255
351890
3519285
352060
3521105
3522330
3523345
3524120
352575
3526390
3527135
3528420
3529435
353030

FAQ

What's the Least Common Multiple (LCM) of 3, 5 and 10?

LCM of 3, 5 and 10 is 30

How to find the LCM of 3, 5 and 10 by prime factorization?

Take every prime that appears in 3, 5 and 10 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5 = 30.

Can you get the LCM of 3, 5 and 10 two numbers at a time?

Yes. The LCM of 3 and 5 is 15, and the LCM of 15 and 10 is 30 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 30 divisible by 3, 5 and 10?

Yes, and by definition it is the smallest positive integer that is: 30 ÷ 3, 30 ÷ 5 and 30 ÷ 10 all come out whole. Any other common multiple of 3, 5 and 10 is a multiple of 30.

See Also