LCM for 14, 24 and 28

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What's the Least Common Multiple (LCM) of 14, 24 and 28?

Answer

LCM of 14, 24 and 28 is
168

First common multiples: 168, 336, 504, …

168 is divisible by all three: 168 ÷ 14 = 12, 168 ÷ 24 = 7, 168 ÷ 28 = 6 — and 12, 7 and 6 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 12 and of y/24 by 7 and of z/28 by 6.

14 = 2 × 7

24 = 23 × 3

28 = 22 × 7

Prime142428Highest power
22232223
3—3—3
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 × 3 × 7 = 168

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LCM Table

1st2nd3rdLCM
1314242,184
141424168
141524840
141624336
1417242,856
141824504
1419243,192
142024840
142124168
1422241,848
1423243,864
142424168
1424254,200
1424262,184
1424271,512
142428168
1424294,872
142430840
1424315,208
142432672
1424331,848
1424342,856
142435840
142436504
1424376,216
1424383,192
1424392,184
142440840
1424416,888
142442168

FAQ

What's the Least Common Multiple (LCM) of 14, 24 and 28?

LCM of 14, 24 and 28 is 168

How to find the LCM of 14, 24 and 28 by prime factorization?

Take every prime that appears in 14, 24 and 28 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 14, 24 and 28 two numbers at a time?

Yes. The LCM of 14 and 24 is 168, and the LCM of 168 and 28 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 14, 24 and 28?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 14, 168 ÷ 24 and 168 ÷ 28 all come out whole. Any other common multiple of 14, 24 and 28 is a multiple of 168.

See Also