LCM for 8, 12 and 36

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What's the Least Common Multiple (LCM) of 8, 12 and 36?

Answer

LCM of 8, 12 and 36 is
72

First common multiples: 72, 144, 216, …

72 is divisible by all three: 72 ÷ 8 = 9, 72 ÷ 12 = 6, 72 ÷ 36 = 2 — and 9, 6 and 2 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 9 and of y/12 by 6 and of z/36 by 2.

8 = 23

12 = 22 × 3

36 = 22 × 32

Prime81236Highest power
223222223
3—33232

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

LCM = 23 × 32 = 72

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LCM Table

1st2nd3rdLCM
81221168
81222264
81223552
8122424
81225600
81226312
81227216
81228168
81229696
81230120
81231744
8123296
81233264
81234408
81235840
8123672
81237888
81238456
81239312
81240120
81241984
81242168
812431,032
81244264
81245360
81246552
812471,128
8124848
812491,176
81250600

FAQ

What's the Least Common Multiple (LCM) of 8, 12 and 36?

LCM of 8, 12 and 36 is 72

How to find the LCM of 8, 12 and 36 by prime factorization?

Take every prime that appears in 8, 12 and 36 to the highest power it reaches in any one of them and multiply: 2³ × 3² = 72.

Can you get the LCM of 8, 12 and 36 two numbers at a time?

Yes. The LCM of 8 and 12 is 24, and the LCM of 24 and 36 is 72 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 72 divisible by 8, 12 and 36?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 8, 72 ÷ 12 and 72 ÷ 36 all come out whole. Any other common multiple of 8, 12 and 36 is a multiple of 72.

See Also