LCM for 25, 45 and 60

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 25, 45 and 60?

Answer

LCM of 25, 45 and 60 is
900

(Nine hundred)

900 is the smallest positive integer that 25, 45 and 60 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 25, 45 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 45: 3 × 3 × 5 (exponent form: 32 × 5)

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

Prime factor254560Highest power
2——2222
3—32332
5525552

LCM = 22 × 32 × 52 = 900

Checking the LCM of 25, 45 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, 45) = (25 × 45) ÷ 5 = 1,125 ÷ 5 = 225

LCM(225, 60) = (225 × 60) ÷ 15 = 13,500 ÷ 15 = 900

LCM(25, 45, 60) = 900

The pairs may be taken in any order — 45 and 60 first, then 25 — and the answer is the same 900. 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 25, 45 and 60? (The answer is: 900). Enter the first number (e.g. '25'), the second (e.g. '45') 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
254545225
25454610,350
25454710,575
2545483,600
25454911,025
254550450
2545513,825
25455211,700
25455311,925
2545541,350
2545552,475
25455612,600
2545574,275
25455813,050
25455913,275
254560900
25456113,725
25456213,950
2545631,575
25456414,400
2545652,925
2545664,950
25456715,075
25456815,300
2545695,175
2545703,150
25457115,975
2545721,800
25457316,425
25457416,650

FAQ

What's the Least Common Multiple (LCM) of 25, 45 and 60?

LCM of 25, 45 and 60 is 900

How to find the LCM of 25, 45 and 60 by prime factorization?

Take every prime that appears in 25, 45 and 60 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5² = 900.

Can you get the LCM of 25, 45 and 60 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 25 and 45 is 225, and the LCM of 225 and 60 is 900 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 900 divisible by 25, 45 and 60?

Yes, and by definition it is the smallest positive integer that is: 900 ÷ 25, 900 ÷ 45 and 900 ÷ 60 all come out whole. Any other common multiple of 25, 45 and 60 is a multiple of 900.

See Also