LCM for 7, 8 and 11

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What's the Least Common Multiple (LCM) of 7, 8 and 11?

Answer

LCM of 7, 8 and 11 is
616

First common multiples: 616; 1,232; 1,848; …

616 is divisible by all three: 616 ÷ 7 = 88, 616 ÷ 8 = 77, 616 ÷ 11 = 56 — and 88, 77 and 56 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 88 and of y/8 by 77 and of z/11 by 56.

7 — prime

8 = 23

11 — prime

Prime7811Highest power
2—23—23
77——7
11——1111

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

LCM = 23 × 7 × 11 = 616

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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 11?

LCM of 7, 8 and 11 is 616

How to find the LCM of 7, 8 and 11 by prime factorization?

Take every prime that appears in 7, 8 and 11 to the highest power it reaches in any one of them and multiply: 2³ × 7 × 11 = 616.

Can you get the LCM of 7, 8 and 11 two numbers at a time?

Yes. The LCM of 7 and 8 is 56, and the LCM of 56 and 11 is 616 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 616 divisible by 7, 8 and 11?

Yes, and by definition it is the smallest positive integer that is: 616 ÷ 7, 616 ÷ 8 and 616 ÷ 11 all come out whole. Any other common multiple of 7, 8 and 11 is a multiple of 616.

See Also