LCM for 9, 15 and 25

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 9, 15 and 25?

Answer

LCM of 9, 15 and 25 is
225

(Two hundred twenty-five)

225 is the smallest positive integer that 9, 15 and 25 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 9, 15 and 25 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 15: 3 × 5 (exponent form: 3 × 5)

All Prime Factors of 25: 5 × 5 (exponent form: 52)

Prime factor91525Highest power
3323—32
5—55252

LCM = 32 × 52 = 225

Checking the LCM of 9, 15 and 25 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, 15) = (9 × 15) ÷ 3 = 135 ÷ 3 = 45

LCM(45, 25) = (45 × 25) ÷ 5 = 1,125 ÷ 5 = 225

LCM(9, 15, 25) = 225

The pairs may be taken in any order — 15 and 25 first, then 9 — and the answer is the same 225. 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, 15 and 25? (The answer is: 225). Enter the first number (e.g. '9'), the second (e.g. '15') and the third (e.g. '25'), 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
9101590
91115495
91215180
91315585
91415630
9151545
91516720
91517765
9151890
91519855
91520180
91521315
91522990
915231,035
91524360
91525225
915261,170
91527135
915281,260
915291,305
9153090
915311,395
915321,440
91533495
915341,530
91535315
91536180
915371,665
915381,710
91539585

FAQ

What's the Least Common Multiple (LCM) of 9, 15 and 25?

LCM of 9, 15 and 25 is 225

How to find the LCM of 9, 15 and 25 by prime factorization?

Take every prime that appears in 9, 15 and 25 to the highest power it reaches in any one of them and multiply: 3² × 5² = 225.

Can you get the LCM of 9, 15 and 25 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 9 and 15 is 45, and the LCM of 45 and 25 is 225 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 225 divisible by 9, 15 and 25?

Yes, and by definition it is the smallest positive integer that is: 225 ÷ 9, 225 ÷ 15 and 225 ÷ 25 all come out whole. Any other common multiple of 9, 15 and 25 is a multiple of 225.

See Also