LCM for 15, 25 and 45

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 15, 25 and 45?

Answer

LCM of 15, 25 and 45 is
225

(Two hundred twenty-five)

225 is the smallest positive integer that 15, 25 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 15, 25 and 45 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 15: 3 × 5 (exponent form: 3 × 5)

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

All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

Prime factor152545Highest power
33—3232
5552552

LCM = 32 × 52 = 225

Checking the LCM of 15, 25 and 45 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(15, 25) = (15 × 25) ÷ 5 = 375 ÷ 5 = 75

LCM(75, 45) = (75 × 45) ÷ 15 = 3,375 ÷ 15 = 225

LCM(15, 25, 45) = 225

The pairs may be taken in any order — 25 and 45 first, then 15 — and the answer is the same 225. 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 15, 25 and 45? (The answer is: 225). Enter the first number (e.g. '15'), the second (e.g. '25') and the third (e.g. '45'), 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
152530150
1525312,325
1525322,400
152533825
1525342,550
152535525
152536900
1525372,775
1525382,850
152539975
152540600
1525413,075
1525421,050
1525433,225
1525443,300
152545225
1525463,450
1525473,525
1525481,200
1525493,675
152550150
1525511,275
1525523,900
1525533,975
1525541,350
152555825
1525564,200
1525571,425
1525584,350
1525594,425

FAQ

What's the Least Common Multiple (LCM) of 15, 25 and 45?

LCM of 15, 25 and 45 is 225

How to find the LCM of 15, 25 and 45 by prime factorization?

Take every prime that appears in 15, 25 and 45 to the highest power it reaches in any one of them and multiply: 3² × 5² = 225.

Can you get the LCM of 15, 25 and 45 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 15 and 25 is 75, and the LCM of 75 and 45 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 15, 25 and 45?

Yes, and by definition it is the smallest positive integer that is: 225 ÷ 15, 225 ÷ 25 and 225 ÷ 45 all come out whole. Any other common multiple of 15, 25 and 45 is a multiple of 225.

See Also