LCM for 9, 12 and 15

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

What's the Least Common Multiple (LCM) of 9, 12 and 15?

Answer

LCM of 9, 12 and 15 is
180

(One hundred eighty)

180 is the smallest positive integer that 9, 12 and 15 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 9, 12 and 15 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 9: 3 × 3 (exponent form: 32)

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

All Prime Factors of 15: 3 × 5 (exponent form: 3 × 5)

Prime factor91215Highest power
2—22—22
3323332
5——55

LCM = 22 × 32 × 5 = 180

Checking the LCM of 9, 12 and 15 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(9, 12) = (9 × 12) ÷ 3 = 108 ÷ 3 = 36

LCM(36, 15) = (36 × 15) ÷ 3 = 540 ÷ 3 = 180

LCM(9, 12, 15) = 180

The pairs may be taken in any order — 12 and 15 first, then 9 — 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 9, 12 and 15? (The answer is: 180). Enter the first number (e.g. '9'), the second (e.g. '12') and the third (e.g. '15'), 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
191236
291236
391236
491236
5912180
691236
7912252
891272
991236
91012180
91112396
9121236
91213468
91214252
91215180
91216144
91217612
9121836
91219684
91220180
91221252
91222396
91223828
9122472
91225900
91226468
91227108
91228252
912291,044
91230180

FAQ

What's the Least Common Multiple (LCM) of 9, 12 and 15?

LCM of 9, 12 and 15 is 180

How to find the LCM of 9, 12 and 15 by prime factorization?

Take every prime that appears in 9, 12 and 15 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 9, 12 and 15 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 9 and 12 is 36, and the LCM of 36 and 15 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 9, 12 and 15?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 9, 180 ÷ 12 and 180 ÷ 15 all come out whole. Any other common multiple of 9, 12 and 15 is a multiple of 180.

See Also