LCM for 7, 8 and 12

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What's the Least Common Multiple (LCM) of 7, 8 and 12?

Answer

LCM of 7, 8 and 12 is
168

First common multiples: 168, 336, 504, …

168 is divisible by all three: 168 ÷ 7 = 24, 168 ÷ 8 = 21, 168 ÷ 12 = 14 — and 24, 21 and 14 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/7 by 24 and of y/8 by 21 and of z/12 by 14.

7 — prime

8 = 23

12 = 22 × 3

Prime7812Highest power
2—232223
3——33
77——7

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

LCM = 23 × 3 × 7 = 168

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LCM Table

1st2nd3rdLCM
17856
27856
378168
47856
578280
678168
77856
78856
789504
7810280
7811616
7812168
7813728
781456
7815840
7816112
7817952
7818504
78191,064
7820280
7821168
7822616
78231,288
7824168
78251,400
7826728
78271,512
782856
78291,624
7830840

FAQ

What's the Least Common Multiple (LCM) of 7, 8 and 12?

LCM of 7, 8 and 12 is 168

How to find the LCM of 7, 8 and 12 by prime factorization?

Take every prime that appears in 7, 8 and 12 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 7, 8 and 12 two numbers at a time?

Yes. The LCM of 7 and 8 is 56, and the LCM of 56 and 12 is 168 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 168 divisible by 7, 8 and 12?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 7, 168 ÷ 8 and 168 ÷ 12 all come out whole. Any other common multiple of 7, 8 and 12 is a multiple of 168.

See Also