LCM for 8, 12 and 20

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What's the Least Common Multiple (LCM) of 8, 12 and 20?

Answer

LCM of 8, 12 and 20 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 8 = 15, 120 ÷ 12 = 10, 120 ÷ 20 = 6 — and 15, 10 and 6 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 15 and of y/12 by 10 and of z/20 by 6.

8 = 23

12 = 22 × 3

20 = 22 × 5

Prime81220Highest power
223222223
3—3—3
5——55

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

LCM = 23 × 3 × 5 = 120

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LCM Table

1st2nd3rdLCM
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
81231744
8123296
81233264
81234408

FAQ

What's the Least Common Multiple (LCM) of 8, 12 and 20?

LCM of 8, 12 and 20 is 120

How to find the LCM of 8, 12 and 20 by prime factorization?

Take every prime that appears in 8, 12 and 20 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 8, 12 and 20 two numbers at a time?

Yes. The LCM of 8 and 12 is 24, and the LCM of 24 and 20 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 8, 12 and 20?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 8, 120 ÷ 12 and 120 ÷ 20 all come out whole. Any other common multiple of 8, 12 and 20 is a multiple of 120.

See Also