LCM for 12, 14 and 84

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Least Common Multiple of
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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

(Eighty-four)

84 is the smallest positive integer that 12, 14 and 84 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 14 and 84 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

All Prime Factors of 14: 2 × 7 (exponent form: 2 × 7)

All Prime Factors of 84: 2 × 2 × 3 × 7 (exponent form: 22 × 3 × 7)

Prime factor121484Highest power
22222222
33—33
7—777

LCM = 22 × 3 × 7 = 84

Checking the LCM of 12, 14 and 84 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(12, 14) = (12 × 14) ÷ 2 = 168 ÷ 2 = 84

LCM(84, 84) = (84 × 84) ÷ 84 = 7,056 ÷ 84 = 84

LCM(12, 14, 84) = 84

The pairs may be taken in any order — 14 and 84 first, then 12 — and the answer is the same 84. That is exactly why the two routes on this page agree.

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About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 12, 14 and 84? (The answer is: 84). Enter the first number (e.g. '12'), the second (e.g. '14') and the third (e.g. '84'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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LCM Table

Number 1Number 2Number 3LCM
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, and it is the check this page prints. 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.

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