LCM for 4, 12 and 14

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What's the Least Common Multiple (LCM) of 4, 12 and 14?

Answer

LCM of 4, 12 and 14 is
84

First common multiples: 84, 168, 252, …

84 is divisible by all three: 84 ÷ 4 = 21, 84 ÷ 12 = 7, 84 ÷ 14 = 6 — and 21, 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/4 by 21 and of y/12 by 7 and of z/14 by 6.

4 = 22

12 = 22 × 3

14 = 2 × 7

Prime41214Highest power
22222222
3—3—3
7——77

— = 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
141212
241212
341212
441212
451260
461212
471284
481224
491236
4101260
41112132
4121212
41213156
4121484
4121560
4121648
41217204
4121836
41219228
4122060
4122184
41222132
41223276
4122424
41225300
41226156
41227108
4122884
41229348
4123060

FAQ

What's the Least Common Multiple (LCM) of 4, 12 and 14?

LCM of 4, 12 and 14 is 84

How to find the LCM of 4, 12 and 14 by prime factorization?

Take every prime that appears in 4, 12 and 14 to the highest power it reaches in any one of them and multiply: 2² × 3 × 7 = 84.

Can you get the LCM of 4, 12 and 14 two numbers at a time?

Yes. The LCM of 4 and 12 is 12, and the LCM of 12 and 14 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 4, 12 and 14?

Yes, and by definition it is the smallest positive integer that is: 84 ÷ 4, 84 ÷ 12 and 84 ÷ 14 all come out whole. Any other common multiple of 4, 12 and 14 is a multiple of 84.

See Also