LCM for 5, 9 and 15

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

What's the Least Common Multiple (LCM) of 5, 9 and 15?

Answer

LCM of 5, 9 and 15 is
45

(Forty-five)

45 is the smallest positive integer that 5, 9 and 15 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 5, 9 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 5: 5 (exponent form: 5)

All Prime Factors of 9: 3 × 3 (exponent form: 32)

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

Prime factor5915Highest power
3—32332
55—55

LCM = 32 × 5 = 45

Checking the LCM of 5, 9 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(5, 9) = (5 × 9) ÷ 1 = 45 ÷ 1 = 45

LCM(45, 15) = (45 × 15) ÷ 15 = 675 ÷ 15 = 45

LCM(5, 9, 15) = 45

The pairs may be taken in any order — 9 and 15 first, then 5 — and the answer is the same 45. That is exactly why the two routes on this page agree.

Related Calculations

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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 5, 9 and 15? (The answer is: 45). Enter the first number (e.g. '5'), the second (e.g. '9') 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
15945
25990
35945
459180
55945
56990
579315
589360
59945
591090
5911495
5912180
5913585
5914630
591545
5916720
5917765
591890
5919855
5920180
5921315
5922990
59231,035
5924360
5925225
59261,170
5927135
59281,260
59291,305
593090

FAQ

What's the Least Common Multiple (LCM) of 5, 9 and 15?

LCM of 5, 9 and 15 is 45

How to find the LCM of 5, 9 and 15 by prime factorization?

Take every prime that appears in 5, 9 and 15 to the highest power it reaches in any one of them and multiply: 3² × 5 = 45.

Can you get the LCM of 5, 9 and 15 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 5 and 9 is 45, and the LCM of 45 and 15 is 45 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 45 divisible by 5, 9 and 15?

Yes, and by definition it is the smallest positive integer that is: 45 ÷ 5, 45 ÷ 9 and 45 ÷ 15 all come out whole. Any other common multiple of 5, 9 and 15 is a multiple of 45.

See Also