LCM for 12, 15 and 60

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

What's the Least Common Multiple (LCM) of 12, 15 and 60?

Answer

LCM of 12, 15 and 60 is
60

(Sixty)

60 is the smallest positive integer that 12, 15 and 60 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 15 and 60 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 15: 3 × 5 (exponent form: 3 × 5)

All Prime Factors of 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

Prime factor121560Highest power
222—2222
33333
5—555

LCM = 22 × 3 × 5 = 60

Checking the LCM of 12, 15 and 60 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, 15) = (12 × 15) ÷ 3 = 180 ÷ 3 = 60

LCM(60, 60) = (60 × 60) ÷ 60 = 3,600 ÷ 60 = 60

LCM(12, 15, 60) = 60

The pairs may be taken in any order — 15 and 60 first, then 12 — and the answer is the same 60. That is exactly why the two routes on this page agree.

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See Also

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, 15 and 60? (The answer is: 60). Enter the first number (e.g. '12'), the second (e.g. '15') and the third (e.g. '60'), 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
121545180
1215461,380
1215472,820
121548240
1215492,940
121550300
1215511,020
121552780
1215533,180
121554540
121555660
121556840
1215571,140
1215581,740
1215593,540
12156060
1215613,660
1215621,860
1215631,260
121564960
121565780
121566660
1215674,020
1215681,020
1215691,380
121570420
1215714,260
121572360
1215734,380
1215742,220

FAQ

What's the Least Common Multiple (LCM) of 12, 15 and 60?

LCM of 12, 15 and 60 is 60

How to find the LCM of 12, 15 and 60 by prime factorization?

Take every prime that appears in 12, 15 and 60 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 12, 15 and 60 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 12 and 15 is 60, and the LCM of 60 and 60 is 60 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 60 divisible by 12, 15 and 60?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 12, 60 ÷ 15 and 60 ÷ 60 all come out whole. Any other common multiple of 12, 15 and 60 is a multiple of 60.

See Also