LCM for 25, 50 and 75

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

What's the Least Common Multiple (LCM) of 25, 50 and 75?

Answer

LCM of 25, 50 and 75 is
150

(One hundred fifty)

150 is the smallest positive integer that 25, 50 and 75 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 25, 50 and 75 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 50: 2 × 5 × 5 (exponent form: 2 × 52)

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

Prime factor255075Highest power
2—2—2
3——33
552525252

LCM = 2 × 3 × 52 = 150

Checking the LCM of 25, 50 and 75 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, 50) = (25 × 50) ÷ 25 = 1,250 ÷ 25 = 50

LCM(50, 75) = (50 × 75) ÷ 25 = 3,750 ÷ 25 = 150

LCM(25, 50, 75) = 150

The pairs may be taken in any order — 50 and 75 first, then 25 — and the answer is the same 150. 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, 50 and 75? (The answer is: 150). Enter the first number (e.g. '25'), the second (e.g. '50') and the third (e.g. '75'), 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
255060300
2550613,050
2550621,550
2550633,150
2550641,600
255065650
2550661,650
2550673,350
2550681,700
2550693,450
255070350
2550713,550
2550721,800
2550733,650
2550741,850
255075150
2550761,900
2550773,850
2550781,950
2550793,950
255080400
2550814,050
2550822,050
2550834,150
2550842,100
255085850
2550862,150
2550874,350
2550882,200
2550894,450

FAQ

What's the Least Common Multiple (LCM) of 25, 50 and 75?

LCM of 25, 50 and 75 is 150

How to find the LCM of 25, 50 and 75 by prime factorization?

Take every prime that appears in 25, 50 and 75 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5² = 150.

Can you get the LCM of 25, 50 and 75 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 25 and 50 is 50, and the LCM of 50 and 75 is 150 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 150 divisible by 25, 50 and 75?

Yes, and by definition it is the smallest positive integer that is: 150 ÷ 25, 150 ÷ 50 and 150 ÷ 75 all come out whole. Any other common multiple of 25, 50 and 75 is a multiple of 150.

See Also