LCM for 3, 5 and 11

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What's the Least Common Multiple (LCM) of 3, 5 and 11?

Answer

LCM of 3, 5 and 11 is
165

First common multiples: 165, 330, 495, …

165 is divisible by all three: 165 ÷ 3 = 55, 165 ÷ 5 = 33, 165 ÷ 11 = 15 — and 55, 33 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 55 and of y/5 by 33 and of z/11 by 15.

3 — prime

5 — prime

11 — prime

Prime3511Highest power
33——3
5—5—5
11——1111

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

LCM = 3 × 5 × 11 = 165

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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 11?

LCM of 3, 5 and 11 is 165

How to find the LCM of 3, 5 and 11 by prime factorization?

Take every prime that appears in 3, 5 and 11 to the highest power it reaches in any one of them and multiply: 3 × 5 × 11 = 165.

Can you get the LCM of 3, 5 and 11 two numbers at a time?

Yes. The LCM of 3 and 5 is 15, and the LCM of 15 and 11 is 165 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 165 divisible by 3, 5 and 11?

Yes, and by definition it is the smallest positive integer that is: 165 ÷ 3, 165 ÷ 5 and 165 ÷ 11 all come out whole. Any other common multiple of 3, 5 and 11 is a multiple of 165.

See Also