LCM for 12, 14 and 84

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What's the Least Common Multiple (LCM) of 12, 14 and 84?

Answer

LCM of 12, 14 and 84 is
84

First common multiples: 84, 168, 252, …

84 is divisible by all three: 84 ÷ 12 = 7, 84 ÷ 14 = 6, 84 ÷ 84 = 1 — and 7, 6 and 1 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/12 by 7 and of y/14 by 6.

12 = 22 × 3

14 = 2 × 7

84 = 22 × 3 × 7

Prime121484Highest power
22222222
33—33
7—777

— = 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
1214691,932
121470420
1214715,964
121472504
1214736,132
1214743,108
1214752,100
1214761,596
121477924
1214781,092
1214796,636
1214801,680
1214812,268
1214823,444
1214836,972
12148484
1214857,140
1214863,612
1214872,436
1214881,848
1214897,476
1214901,260
1214911,092
1214921,932
1214932,604
1214943,948
1214957,980
121496672
1214978,148
121498588

FAQ

What's the Least Common Multiple (LCM) of 12, 14 and 84?

LCM of 12, 14 and 84 is 84

How to find the LCM of 12, 14 and 84 by prime factorization?

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

Can you get the LCM of 12, 14 and 84 two numbers at a time?

Yes. The LCM of 12 and 14 is 84, and the LCM of 84 and 84 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 12, 14 and 84?

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

See Also