LCM for 8, 14 and 28

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What's the Least Common Multiple (LCM) of 8, 14 and 28?

Answer

LCM of 8, 14 and 28 is
56

First common multiples: 56, 112, 168, …

56 is divisible by all three: 56 ÷ 8 = 7, 56 ÷ 14 = 4, 56 ÷ 28 = 2 — and 7, 4 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 7 and of y/14 by 4 and of z/28 by 2.

8 = 23

14 = 2 × 7

28 = 22 × 7

Prime81428Highest power
22322223
7—777

— = 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
81314728
8141456
81415840
81416112
81417952
81418504
814191,064
81420280
81421168
81422616
814231,288
81424168
814251,400
81426728
814271,512
8142856
814291,624
81430840
814311,736
81432224
814331,848
81434952
81435280
81436504
814372,072
814381,064
814392,184
81440280
814412,296
81442168

FAQ

What's the Least Common Multiple (LCM) of 8, 14 and 28?

LCM of 8, 14 and 28 is 56

How to find the LCM of 8, 14 and 28 by prime factorization?

Take every prime that appears in 8, 14 and 28 to the highest power it reaches in any one of them and multiply: 2³ × 7 = 56.

Can you get the LCM of 8, 14 and 28 two numbers at a time?

Yes. The LCM of 8 and 14 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 8, 14 and 28?

Yes, and by definition it is the smallest positive integer that is: 56 ÷ 8, 56 ÷ 14 and 56 ÷ 28 all come out whole. Any other common multiple of 8, 14 and 28 is a multiple of 56.

See Also