LCM for 14, 21 and 28

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What's the Least Common Multiple (LCM) of 14, 21 and 28?

Answer

LCM of 14, 21 and 28 is
84

First common multiples: 84, 168, 252, …

84 is divisible by all three: 84 ÷ 14 = 6, 84 ÷ 21 = 4, 84 ÷ 28 = 3 — and 6, 4 and 3 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/14 by 6 and of y/21 by 4 and of z/28 by 3.

14 = 2 × 7

21 = 3 × 7

28 = 22 × 7

Prime142128Highest power
22—2222
3—3—3
77777

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

LCM = 22 × 3 × 7 = 84

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LCM Table

1st2nd3rdLCM
131421546
14142142
141521210
141621336
141721714
141821126
141921798
142021420
14212142
142122462
142123966
142124168
1421251,050
142126546
142127378
14212884
1421291,218
142130210
1421311,302
142132672
142133462
142134714
142135210
142136252
1421371,554
142138798
142139546
142140840
1421411,722
14214242

FAQ

What's the Least Common Multiple (LCM) of 14, 21 and 28?

LCM of 14, 21 and 28 is 84

How to find the LCM of 14, 21 and 28 by prime factorization?

Take every prime that appears in 14, 21 and 28 to the highest power it reaches in any one of them and multiply: 2² × 3 × 7 = 84.

Can you get the LCM of 14, 21 and 28 two numbers at a time?

Yes. The LCM of 14 and 21 is 42, and the LCM of 42 and 28 is 84 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 84 divisible by 14, 21 and 28?

Yes, and by definition it is the smallest positive integer that is: 84 ÷ 14, 84 ÷ 21 and 84 ÷ 28 all come out whole. Any other common multiple of 14, 21 and 28 is a multiple of 84.

See Also