LCM for 25, 30 and 40

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

What's the Least Common Multiple (LCM) of 25, 30 and 40?

Answer

LCM of 25, 30 and 40 is
600

(Six hundred)

600 is the smallest positive integer that 25, 30 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 25, 30 and 40 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

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

Prime factor253040Highest power
2—22323
3—3—3
5525552

LCM = 23 × 3 × 52 = 600

Checking the LCM of 25, 30 and 40 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, 30) = (25 × 30) ÷ 5 = 750 ÷ 5 = 150

LCM(150, 40) = (150 × 40) ÷ 10 = 6,000 ÷ 10 = 600

LCM(25, 30, 40) = 600

The pairs may be taken in any order — 30 and 40 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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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 25, 30 and 40? (The answer is: 600). Enter the first number (e.g. '25'), the second (e.g. '30') and the third (e.g. '40'), 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
252530150
2526301,950
2527301,350
2528302,100
2529304,350
253030150
2530314,650
2530322,400
2530331,650
2530342,550
2530351,050
253036900
2530375,550
2530382,850
2530391,950
253040600
2530416,150
2530421,050
2530436,450
2530443,300
253045450
2530463,450
2530477,050
2530481,200
2530497,350
253050150
2530512,550
2530523,900
2530537,950
2530541,350

FAQ

What's the Least Common Multiple (LCM) of 25, 30 and 40?

LCM of 25, 30 and 40 is 600

How to find the LCM of 25, 30 and 40 by prime factorization?

Take every prime that appears in 25, 30 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5² = 600.

Can you get the LCM of 25, 30 and 40 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 25 and 30 is 150, and the LCM of 150 and 40 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, 30 and 40?

Yes, and by definition it is the smallest positive integer that is: 600 ÷ 25, 600 ÷ 30 and 600 ÷ 40 all come out whole. Any other common multiple of 25, 30 and 40 is a multiple of 600.

See Also