LCM for 6, 10 and 16

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What's the Least Common Multiple (LCM) of 6, 10 and 16?

Answer

LCM of 6, 10 and 16 is
240

First common multiples: 240, 480, 720, …

240 is divisible by all three: 240 ÷ 6 = 40, 240 ÷ 10 = 24, 240 ÷ 16 = 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/6 by 40 and of y/10 by 24 and of z/16 by 15.

6 = 2 × 3

10 = 2 × 5

16 = 24

Prime61016Highest power
2222424
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 = 24 × 3 × 5 = 240

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LCM Table

1st2nd3rdLCM
161030
261030
361030
461060
561030
661030
6710210
6810120
691090
6101030
61011330
6101260
61013390
61014210
6101530
61016240
61017510
6101890
61019570
6102060
61021210
61022330
61023690
61024120
61025150
61026390
61027270
61028420
61029870
6103030

FAQ

What's the Least Common Multiple (LCM) of 6, 10 and 16?

LCM of 6, 10 and 16 is 240

How to find the LCM of 6, 10 and 16 by prime factorization?

Take every prime that appears in 6, 10 and 16 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 5 = 240.

Can you get the LCM of 6, 10 and 16 two numbers at a time?

Yes. The LCM of 6 and 10 is 30, and the LCM of 30 and 16 is 240 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 240 divisible by 6, 10 and 16?

Yes, and by definition it is the smallest positive integer that is: 240 ÷ 6, 240 ÷ 10 and 240 ÷ 16 all come out whole. Any other common multiple of 6, 10 and 16 is a multiple of 240.

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