LCM for 6, 15 and 25

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

What's the Least Common Multiple (LCM) of 6, 15 and 25?

Answer

LCM of 6, 15 and 25 is
150

(One hundred fifty)

150 is the smallest positive integer that 6, 15 and 25 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 6, 15 and 25 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 6: 2 × 3 (exponent form: 2 × 3)

All Prime Factors of 15: 3 × 5 (exponent form: 3 × 5)

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

Prime factor61525Highest power
22——2
333—3
5—55252

LCM = 2 × 3 × 52 = 150

Checking the LCM of 6, 15 and 25 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(6, 15) = (6 × 15) ÷ 3 = 90 ÷ 3 = 30

LCM(30, 25) = (30 × 25) ÷ 5 = 750 ÷ 5 = 150

LCM(6, 15, 25) = 150

The pairs may be taken in any order — 15 and 25 first, then 6 — and the answer is the same 150. That is exactly why the two routes on this page agree.

Related Calculations

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 6, 15 and 25? (The answer is: 150). Enter the first number (e.g. '6'), the second (e.g. '15') and the third (e.g. '25'), 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
6101530
61115330
6121560
61315390
61415210
6151530
61516240
61517510
6151890
61519570
6152060
61521210
61522330
61523690
61524120
61525150
61526390
61527270
61528420
61529870
6153030
61531930
61532480
61533330
61534510
61535210
61536180
615371,110
61538570
61539390

FAQ

What's the Least Common Multiple (LCM) of 6, 15 and 25?

LCM of 6, 15 and 25 is 150

How to find the LCM of 6, 15 and 25 by prime factorization?

Take every prime that appears in 6, 15 and 25 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5² = 150.

Can you get the LCM of 6, 15 and 25 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 6 and 15 is 30, and the LCM of 30 and 25 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 6, 15 and 25?

Yes, and by definition it is the smallest positive integer that is: 150 ÷ 6, 150 ÷ 15 and 150 ÷ 25 all come out whole. Any other common multiple of 6, 15 and 25 is a multiple of 150.

See Also