LCM for 15, 25 and 75

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 15, 25 and 75?

Answer

LCM of 15, 25 and 75 is
75

(Seventy-five)

75 is the smallest positive integer that 15, 25 and 75 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 15, 25 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 15: 3 × 5 (exponent form: 3 × 5)

All Prime Factors of 25: 5 × 5 (exponent form: 52)

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

Prime factor152575Highest power
33—33
55525252

LCM = 3 × 52 = 75

Checking the LCM of 15, 25 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(15, 25) = (15 × 25) ÷ 5 = 375 ÷ 5 = 75

LCM(75, 75) = (75 × 75) ÷ 75 = 5,625 ÷ 75 = 75

LCM(15, 25, 75) = 75

The pairs may be taken in any order — 25 and 75 first, then 15 — and the answer is the same 75. 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 15, 25 and 75? (The answer is: 75). Enter the first number (e.g. '15'), the second (e.g. '25') 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
152560300
1525614,575
1525624,650
1525631,575
1525644,800
152565975
1525661,650
1525675,025
1525685,100
1525691,725
1525701,050
1525715,325
1525721,800
1525735,475
1525745,550
15257575
1525765,700
1525775,775
1525781,950
1525795,925
1525801,200
1525812,025
1525826,150
1525836,225
1525842,100
1525851,275
1525866,450
1525872,175
1525886,600
1525896,675

FAQ

What's the Least Common Multiple (LCM) of 15, 25 and 75?

LCM of 15, 25 and 75 is 75

How to find the LCM of 15, 25 and 75 by prime factorization?

Take every prime that appears in 15, 25 and 75 to the highest power it reaches in any one of them and multiply: 3 × 5² = 75.

Can you get the LCM of 15, 25 and 75 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 15 and 25 is 75, and the LCM of 75 and 75 is 75 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 75 divisible by 15, 25 and 75?

Yes, and by definition it is the smallest positive integer that is: 75 ÷ 15, 75 ÷ 25 and 75 ÷ 75 all come out whole. Any other common multiple of 15, 25 and 75 is a multiple of 75.

See Also