LCM for 15, 20 and 25

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

What's the Least Common Multiple (LCM) of 15, 20 and 25?

Answer

LCM of 15, 20 and 25 is
300

(Three hundred)

300 is the smallest positive integer that 15, 20 and 25 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 15, 20 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 15: 3 × 5 (exponent form: 3 × 5)

All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

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

Prime factor152025Highest power
2—22—22
33——3
5555252

LCM = 22 × 3 × 52 = 300

Checking the LCM of 15, 20 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(15, 20) = (15 × 20) ÷ 5 = 300 ÷ 5 = 60

LCM(60, 25) = (60 × 25) ÷ 5 = 1,500 ÷ 5 = 300

LCM(15, 20, 25) = 300

The pairs may be taken in any order — 20 and 25 first, then 15 — and the answer is the same 300. That is exactly why the two routes on this page agree.

Related Calculations

See Also

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, 20 and 25? (The answer is: 300). Enter the first number (e.g. '15'), the second (e.g. '20') 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
10152060
111520660
12152060
131520780
141520420
15152060
151620240
1517201,020
151820180
1519201,140
15202060
152021420
152022660
1520231,380
152024120
152025300
152026780
152027540
152028420
1520291,740
15203060
1520311,860
152032480
152033660
1520341,020
152035420
152036180
1520372,220
1520381,140
152039780

FAQ

What's the Least Common Multiple (LCM) of 15, 20 and 25?

LCM of 15, 20 and 25 is 300

How to find the LCM of 15, 20 and 25 by prime factorization?

Take every prime that appears in 15, 20 and 25 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

Can you get the LCM of 15, 20 and 25 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 15 and 20 is 60, and the LCM of 60 and 25 is 300 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 300 divisible by 15, 20 and 25?

Yes, and by definition it is the smallest positive integer that is: 300 ÷ 15, 300 ÷ 20 and 300 ÷ 25 all come out whole. Any other common multiple of 15, 20 and 25 is a multiple of 300.

See Also