LCM for 25, 45 and 50

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

What's the Least Common Multiple (LCM) of 25, 45 and 50?

Answer

LCM of 25, 45 and 50 is
450

(Four hundred fifty)

450 is the smallest positive integer that 25, 45 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 25, 45 and 50 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 50: 2 × 5 × 5 (exponent form: 2 × 52)

Prime factor254550Highest power
2——22
3—32—32
55255252

LCM = 2 × 32 × 52 = 450

Checking the LCM of 25, 45 and 50 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, 50) = (225 × 50) ÷ 25 = 11,250 ÷ 25 = 450

LCM(25, 45, 50) = 450

The pairs may be taken in any order — 45 and 50 first, then 25 — and the answer is the same 450. 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, 45 and 50? (The answer is: 450). Enter the first number (e.g. '25'), the second (e.g. '45') and the third (e.g. '50'), 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
2535451,575
253645900
2537458,325
2538458,550
2539452,925
2540451,800
2541459,225
2542453,150
2543459,675
2544459,900
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

FAQ

What's the Least Common Multiple (LCM) of 25, 45 and 50?

LCM of 25, 45 and 50 is 450

How to find the LCM of 25, 45 and 50 by prime factorization?

Take every prime that appears in 25, 45 and 50 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5² = 450.

Can you get the LCM of 25, 45 and 50 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 50 is 450 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 450 divisible by 25, 45 and 50?

Yes, and by definition it is the smallest positive integer that is: 450 ÷ 25, 450 ÷ 45 and 450 ÷ 50 all come out whole. Any other common multiple of 25, 45 and 50 is a multiple of 450.

See Also