LCM for 6, 12 and 16

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What's the Least Common Multiple (LCM) of 6, 12 and 16?

Answer

LCM of 6, 12 and 16 is
48

First common multiples: 48, 96, 144, …

48 is divisible by all three: 48 ÷ 6 = 8, 48 ÷ 12 = 4, 48 ÷ 16 = 3 — and 8, 4 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/6 by 8 and of y/12 by 4 and of z/16 by 3.

6 = 2 × 3

12 = 22 × 3

16 = 24

Prime61216Highest power
22222424
333—3

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

LCM = 24 × 3 = 48

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LCM Table

1st2nd3rdLCM
161212
261212
361212
461212
561260
661212
671284
681224
691236
6101260
61112132
6121212
61213156
6121484
6121560
6121648
61217204
6121836
61219228
6122060
6122184
61222132
61223276
6122424
61225300
61226156
61227108
6122884
61229348
6123060

FAQ

What's the Least Common Multiple (LCM) of 6, 12 and 16?

LCM of 6, 12 and 16 is 48

How to find the LCM of 6, 12 and 16 by prime factorization?

Take every prime that appears in 6, 12 and 16 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 = 48.

Can you get the LCM of 6, 12 and 16 two numbers at a time?

Yes. The LCM of 6 and 12 is 12, and the LCM of 12 and 16 is 48 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 48 divisible by 6, 12 and 16?

Yes, and by definition it is the smallest positive integer that is: 48 ÷ 6, 48 ÷ 12 and 48 ÷ 16 all come out whole. Any other common multiple of 6, 12 and 16 is a multiple of 48.

See Also