LCM for 25, 35 and 45

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 25, 35 and 45?

Answer

LCM of 25, 35 and 45 is
1,575

(One thousand five hundred seventy-five)

1,575 is the smallest positive integer that 25, 35 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 25, 35 and 45 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 35: 5 × 7 (exponent form: 5 × 7)

All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

Prime factor253545Highest power
3——3232
5525552
7—7—7

LCM = 32 × 52 × 7 = 1,575

Checking the LCM of 25, 35 and 45 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, 35) = (25 × 35) ÷ 5 = 875 ÷ 5 = 175

LCM(175, 45) = (175 × 45) ÷ 5 = 7,875 ÷ 5 = 1,575

LCM(25, 35, 45) = 1,575

The pairs may be taken in any order — 35 and 45 first, then 25 — and the answer is the same 1,575. 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, 35 and 45? (The answer is: 1,575). Enter the first number (e.g. '25'), the second (e.g. '35') and the third (e.g. '45'), 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
2530351,050
2531355,425
2532355,600
2533355,775
2534355,950
253535175
2535366,300
2535376,475
2535386,650
2535396,825
2535401,400
2535417,175
2535421,050
2535437,525
2535447,700
2535451,575
2535468,050
2535478,225
2535488,400
2535491,225
253550350
2535518,925
2535529,100
2535539,275
2535549,450
2535551,925
2535561,400
2535579,975
25355810,150
25355910,325

FAQ

What's the Least Common Multiple (LCM) of 25, 35 and 45?

LCM of 25, 35 and 45 is 1,575

How to find the LCM of 25, 35 and 45 by prime factorization?

Take every prime that appears in 25, 35 and 45 to the highest power it reaches in any one of them and multiply: 3² × 5² × 7 = 1,575.

Can you get the LCM of 25, 35 and 45 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 25 and 35 is 175, and the LCM of 175 and 45 is 1,575 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,575 divisible by 25, 35 and 45?

Yes, and by definition it is the smallest positive integer that is: 1,575 ÷ 25, 1,575 ÷ 35 and 1,575 ÷ 45 all come out whole. Any other common multiple of 25, 35 and 45 is a multiple of 1,575.

See Also