LCM for 7, 8 and 28

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What's the Least Common Multiple (LCM) of 7, 8 and 28?

Answer

LCM of 7, 8 and 28 is
56

First common multiples: 56, 112, 168, …

56 is divisible by all three: 56 ÷ 7 = 8, 56 ÷ 8 = 7, 56 ÷ 28 = 2 — and 8, 7 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/7 by 8 and of y/8 by 7 and of z/28 by 2.

7 — prime

8 = 23

28 = 22 × 7

Prime7828Highest power
2—232223
77—77

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

LCM = 23 × 7 = 56

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LCM Table

1st2nd3rdLCM
7813728
781456
7815840
7816112
7817952
7818504
78191,064
7820280
7821168
7822616
78231,288
7824168
78251,400
7826728
78271,512
782856
78291,624
7830840
78311,736
7832224
78331,848
7834952
7835280
7836504
78372,072
78381,064
78392,184
7840280
78412,296
7842168

FAQ

What's the Least Common Multiple (LCM) of 7, 8 and 28?

LCM of 7, 8 and 28 is 56

How to find the LCM of 7, 8 and 28 by prime factorization?

Take every prime that appears in 7, 8 and 28 to the highest power it reaches in any one of them and multiply: 2³ × 7 = 56.

Can you get the LCM of 7, 8 and 28 two numbers at a time?

Yes. The LCM of 7 and 8 is 56, and the LCM of 56 and 28 is 56 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 56 divisible by 7, 8 and 28?

Yes, and by definition it is the smallest positive integer that is: 56 ÷ 7, 56 ÷ 8 and 56 ÷ 28 all come out whole. Any other common multiple of 7, 8 and 28 is a multiple of 56.

See Also