LCM for 12, 14 and 20

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

What's the Least Common Multiple (LCM) of 12, 14 and 20?

Answer

LCM of 12, 14 and 20 is
420

(Four hundred twenty)

420 is the smallest positive integer that 12, 14 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 14 and 20 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

Prime factor121420Highest power
22222222
33——3
5——55
7—7—7

LCM = 22 × 3 × 5 × 7 = 420

Checking the LCM of 12, 14 and 20 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, 20) = (84 × 20) ÷ 4 = 1,680 ÷ 4 = 420

LCM(12, 14, 20) = 420

The pairs may be taken in any order — 14 and 20 first, then 12 — and the answer is the same 420. 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 20? (The answer is: 420). Enter the first number (e.g. '12'), the second (e.g. '14') and the third (e.g. '20'), 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
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
1214312,604
121432672
121433924
1214341,428

FAQ

What's the Least Common Multiple (LCM) of 12, 14 and 20?

LCM of 12, 14 and 20 is 420

How to find the LCM of 12, 14 and 20 by prime factorization?

Take every prime that appears in 12, 14 and 20 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 7 = 420.

Can you get the LCM of 12, 14 and 20 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 20 is 420 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 420 divisible by 12, 14 and 20?

Yes, and by definition it is the smallest positive integer that is: 420 ÷ 12, 420 ÷ 14 and 420 ÷ 20 all come out whole. Any other common multiple of 12, 14 and 20 is a multiple of 420.

See Also