LCM for 8, 12 and 16

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What's the Least Common Multiple (LCM) of 8, 12 and 16?

Answer

LCM of 8, 12 and 16 is
48

First common multiples: 48, 96, 144, …

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

8 = 23

12 = 22 × 3

16 = 24

Prime81216Highest power
223222424
3—3—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
181224
281224
381224
481224
5812120
681224
7812168
881224
891272
81012120
81112264
8121224
81213312
81214168
81215120
8121648
81217408
8121872
81219456
81220120
81221168
81222264
81223552
8122424
81225600
81226312
81227216
81228168
81229696
81230120

FAQ

What's the Least Common Multiple (LCM) of 8, 12 and 16?

LCM of 8, 12 and 16 is 48

How to find the LCM of 8, 12 and 16 by prime factorization?

Take every prime that appears in 8, 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 8, 12 and 16 two numbers at a time?

Yes. The LCM of 8 and 12 is 24, and the LCM of 24 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 8, 12 and 16?

Yes, and by definition it is the smallest positive integer that is: 48 ÷ 8, 48 ÷ 12 and 48 ÷ 16 all come out whole. Any other common multiple of 8, 12 and 16 is a multiple of 48.

See Also