LCM for 12, 15 and 18

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

What's the Least Common Multiple (LCM) of 12, 15 and 18?

Answer

LCM of 12, 15 and 18 is
180

(One hundred eighty)

180 is the smallest positive integer that 12, 15 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 15 and 18 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

Prime factor121518Highest power
222—222
3333232
5—5—5

LCM = 22 × 32 × 5 = 180

Checking the LCM of 12, 15 and 18 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, 18) = (60 × 18) ÷ 6 = 1,080 ÷ 6 = 180

LCM(12, 15, 18) = 180

The pairs may be taken in any order — 15 and 18 first, then 12 — and the answer is the same 180. 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, 15 and 18? (The answer is: 180). Enter the first number (e.g. '12'), the second (e.g. '15') and the third (e.g. '18'), 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
3121560
4121560
5121560
6121560
71215420
81215120
91215180
10121560
111215660
12121560
121315780
121415420
12151560
121516240
1215171,020
121518180
1215191,140
12152060
121521420
121522660
1215231,380
121524120
121525300
121526780
121527540
121528420
1215291,740
12153060
1215311,860
121532480

FAQ

What's the Least Common Multiple (LCM) of 12, 15 and 18?

LCM of 12, 15 and 18 is 180

How to find the LCM of 12, 15 and 18 by prime factorization?

Take every prime that appears in 12, 15 and 18 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 12, 15 and 18 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 18 is 180 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 180 divisible by 12, 15 and 18?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 12, 180 ÷ 15 and 180 ÷ 18 all come out whole. Any other common multiple of 12, 15 and 18 is a multiple of 180.

See Also