LCM for 5, 12 and 25

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

What's the Least Common Multiple (LCM) of 5, 12 and 25?

Answer

LCM of 5, 12 and 25 is
300

(Three hundred)

300 is the smallest positive integer that 5, 12 and 25 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 5, 12 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 5: 5 (exponent form: 5)

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

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

Prime factor51225Highest power
2—22—22
3—3—3
55—5252

LCM = 22 × 3 × 52 = 300

Checking the LCM of 5, 12 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(5, 12) = (5 × 12) ÷ 1 = 60 ÷ 1 = 60

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

LCM(5, 12, 25) = 300

The pairs may be taken in any order — 12 and 25 first, then 5 — and the answer is the same 300. That is exactly why the two routes on this page agree.

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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 5, 12 and 25? (The answer is: 300). Enter the first number (e.g. '5'), the second (e.g. '12') 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
5101260
51112660
5121260
51213780
51214420
5121560
51216240
512171,020
51218180
512191,140
5122060
51221420
51222660
512231,380
51224120
51225300
51226780
51227540
51228420
512291,740
5123060
512311,860
51232480
51233660
512341,020
51235420
51236180
512372,220
512381,140
51239780

FAQ

What's the Least Common Multiple (LCM) of 5, 12 and 25?

LCM of 5, 12 and 25 is 300

How to find the LCM of 5, 12 and 25 by prime factorization?

Take every prime that appears in 5, 12 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 5, 12 and 25 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 5 and 12 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 5, 12 and 25?

Yes, and by definition it is the smallest positive integer that is: 300 ÷ 5, 300 ÷ 12 and 300 ÷ 25 all come out whole. Any other common multiple of 5, 12 and 25 is a multiple of 300.

See Also