LCM for 25, 40 and 60

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

What's the Least Common Multiple (LCM) of 25, 40 and 60?

Answer

LCM of 25, 40 and 60 is
600

(Six hundred)

600 is the smallest positive integer that 25, 40 and 60 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 25, 40 and 60 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 25: 5 × 5 (exponent form: 52)

All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

All Prime Factors of 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

Prime factor254060Highest power
2—232223
3——33
5525552

LCM = 23 × 3 × 52 = 600

Checking the LCM of 25, 40 and 60 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(25, 40) = (25 × 40) ÷ 5 = 1,000 ÷ 5 = 200

LCM(200, 60) = (200 × 60) ÷ 20 = 12,000 ÷ 20 = 600

LCM(25, 40, 60) = 600

The pairs may be taken in any order — 40 and 60 first, then 25 — and the answer is the same 600. 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 25, 40 and 60? (The answer is: 600). Enter the first number (e.g. '25'), the second (e.g. '40') and the third (e.g. '60'), 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
2540451,800
2540464,600
2540479,400
2540481,200
2540499,800
254050200
25405110,200
2540522,600
25405310,600
2540545,400
2540552,200
2540561,400
25405711,400
2540585,800
25405911,800
254060600
25406112,200
2540626,200
25406312,600
2540641,600
2540652,600
2540666,600
25406713,400
2540683,400
25406913,800
2540701,400
25407114,200
2540721,800
25407314,600
2540747,400

FAQ

What's the Least Common Multiple (LCM) of 25, 40 and 60?

LCM of 25, 40 and 60 is 600

How to find the LCM of 25, 40 and 60 by prime factorization?

Take every prime that appears in 25, 40 and 60 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5² = 600.

Can you get the LCM of 25, 40 and 60 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 25 and 40 is 200, and the LCM of 200 and 60 is 600 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 600 divisible by 25, 40 and 60?

Yes, and by definition it is the smallest positive integer that is: 600 ÷ 25, 600 ÷ 40 and 600 ÷ 60 all come out whole. Any other common multiple of 25, 40 and 60 is a multiple of 600.

See Also