LCM for 12, 14 and 16

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 12, 14 and 16?

Answer

LCM of 12, 14 and 16 is
336

(Three hundred thirty-six)

336 is the smallest positive integer that 12, 14 and 16 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 14 and 16 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

Prime factor121416Highest power
22222424
33——3
7—7—7

LCM = 24 × 3 × 7 = 336

Checking the LCM of 12, 14 and 16 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, 16) = (84 × 16) ÷ 4 = 1,344 ÷ 4 = 336

LCM(12, 14, 16) = 336

The pairs may be taken in any order — 14 and 16 first, then 12 — and the answer is the same 336. 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 16? (The answer is: 336). Enter the first number (e.g. '12'), the second (e.g. '14') and the third (e.g. '16'), 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
,
and

LCM Table

Number 1Number 2Number 3LCM
1121484
2121484
3121484
4121484
51214420
6121484
7121484
81214168
91214252
101214420
111214924
12121484
1213141,092
12141484
121415420
121416336
1214171,428
121418252
1214191,596
121420420
12142184
121422924
1214231,932
121424168
1214252,100
1214261,092
121427756
12142884
1214292,436
121430420

FAQ

What's the Least Common Multiple (LCM) of 12, 14 and 16?

LCM of 12, 14 and 16 is 336

How to find the LCM of 12, 14 and 16 by prime factorization?

Take every prime that appears in 12, 14 and 16 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 7 = 336.

Can you get the LCM of 12, 14 and 16 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 16 is 336 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 336 divisible by 12, 14 and 16?

Yes, and by definition it is the smallest positive integer that is: 336 ÷ 12, 336 ÷ 14 and 336 ÷ 16 all come out whole. Any other common multiple of 12, 14 and 16 is a multiple of 336.

See Also