LCM for 50, 75 and 125

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 50, 75 and 125?

Answer

LCM of 50, 75 and 125 is
750

(Seven hundred fifty)

750 is the smallest positive integer that 50, 75 and 125 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 50, 75 and 125 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 50: 2 × 5 × 5 (exponent form: 2 × 52)

All Prime Factors of 75: 3 × 5 × 5 (exponent form: 3 × 52)

All Prime Factors of 125: 5 × 5 × 5 (exponent form: 53)

Prime factor5075125Highest power
22——2
3—3—3
552525353

LCM = 2 × 3 × 53 = 750

Checking the LCM of 50, 75 and 125 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(50, 75) = (50 × 75) ÷ 25 = 3,750 ÷ 25 = 150

LCM(150, 125) = (150 × 125) ÷ 25 = 18,750 ÷ 25 = 750

LCM(50, 75, 125) = 750

The pairs may be taken in any order — 75 and 125 first, then 50 — and the answer is the same 750. 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 50, 75 and 125? (The answer is: 750). Enter the first number (e.g. '50'), the second (e.g. '75') and the third (e.g. '125'), 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
50751101,650
50751115,550
50751128,400
507511316,950
50751142,850
50751153,450
50751168,700
50751175,850
50751188,850
507511917,850
5075120600
507512118,150
50751229,150
50751236,150
50751249,300
5075125750
50751263,150
507512719,050
50751289,600
50751296,450
50751301,950
507513119,650
50751323,300
507513319,950
507513410,050
50751351,350
507513610,200
507513720,550
50751383,450
507513920,850

FAQ

What's the Least Common Multiple (LCM) of 50, 75 and 125?

LCM of 50, 75 and 125 is 750

How to find the LCM of 50, 75 and 125 by prime factorization?

Take every prime that appears in 50, 75 and 125 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5³ = 750.

Can you get the LCM of 50, 75 and 125 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 50 and 75 is 150, and the LCM of 150 and 125 is 750 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 750 divisible by 50, 75 and 125?

Yes, and by definition it is the smallest positive integer that is: 750 ÷ 50, 750 ÷ 75 and 750 ÷ 125 all come out whole. Any other common multiple of 50, 75 and 125 is a multiple of 750.

See Also