LCM for 14, 28 and 42

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What's the Least Common Multiple (LCM) of 14, 28 and 42?

Answer

LCM of 14, 28 and 42 is
84

First common multiples: 84, 168, 252, …

84 is divisible by all three: 84 ÷ 14 = 6, 84 ÷ 28 = 3, 84 ÷ 42 = 2 — and 6, 3 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/14 by 6 and of y/28 by 3 and of z/42 by 2.

14 = 2 × 7

28 = 22 × 7

42 = 2 × 3 × 7

Prime142842Highest power
2222222
3——33
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
142728756
14282828
142829812
142830420
142831868
142832224
142833924
142834476
142835140
142836252
1428371,036
142838532
1428391,092
142840280
1428411,148
14284284
1428431,204
142844308
1428451,260
142846644
1428471,316
142848336
142849196
142850700
1428511,428
142852364
1428531,484
142854756
1428551,540
14285656

FAQ

What's the Least Common Multiple (LCM) of 14, 28 and 42?

LCM of 14, 28 and 42 is 84

How to find the LCM of 14, 28 and 42 by prime factorization?

Take every prime that appears in 14, 28 and 42 to the highest power it reaches in any one of them and multiply: 2² × 3 × 7 = 84.

Can you get the LCM of 14, 28 and 42 two numbers at a time?

Yes. The LCM of 14 and 28 is 28, and the LCM of 28 and 42 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, 28 and 42?

Yes, and by definition it is the smallest positive integer that is: 84 ÷ 14, 84 ÷ 28 and 84 ÷ 42 all come out whole. Any other common multiple of 14, 28 and 42 is a multiple of 84.

See Also