LCM for 3, 5 and 8

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 3, 5 and 8?

Answer

LCM of 3, 5 and 8 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 3 = 40, 120 ÷ 5 = 24, 120 ÷ 8 = 15 — and 40, 24 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/3 by 40 and of y/5 by 24 and of z/8 by 15.

3 — prime

5 — prime

8 = 23

Prime358Highest power
2——2323
33——3
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 = 23 × 3 × 5 = 120

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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 8?

LCM of 3, 5 and 8 is 120

How to find the LCM of 3, 5 and 8 by prime factorization?

Take every prime that appears in 3, 5 and 8 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 3, 5 and 8 two numbers at a time?

Yes. The LCM of 3 and 5 is 15, and the LCM of 15 and 8 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 3, 5 and 8?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 3, 120 ÷ 5 and 120 ÷ 8 all come out whole. Any other common multiple of 3, 5 and 8 is a multiple of 120.

See Also