LCM for 6, 10 and 15

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

What's the Least Common Multiple (LCM) of 6, 10 and 15?

Answer

LCM of 6, 10 and 15 is
30

(Thirty)

30 is the smallest positive integer that 6, 10 and 15 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 6, 10 and 15 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 10: 2 × 5 (exponent form: 2 × 5)

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

Prime factor61015Highest power
222—2
33—33
5—555

LCM = 2 × 3 × 5 = 30

Checking the LCM of 6, 10 and 15 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, 10) = (6 × 10) ÷ 2 = 60 ÷ 2 = 30

LCM(30, 15) = (30 × 15) ÷ 15 = 450 ÷ 15 = 30

LCM(6, 10, 15) = 30

The pairs may be taken in any order — 10 and 15 first, then 6 — and the answer is the same 30. 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, 10 and 15? (The answer is: 30). Enter the first number (e.g. '6'), the second (e.g. '10') and the third (e.g. '15'), 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
161030
261030
361030
461060
561030
661030
6710210
6810120
691090
6101030
61011330
6101260
61013390
61014210
6101530
61016240
61017510
6101890
61019570
6102060
61021210
61022330
61023690
61024120
61025150
61026390
61027270
61028420
61029870
6103030

FAQ

What's the Least Common Multiple (LCM) of 6, 10 and 15?

LCM of 6, 10 and 15 is 30

How to find the LCM of 6, 10 and 15 by prime factorization?

Take every prime that appears in 6, 10 and 15 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5 = 30.

Can you get the LCM of 6, 10 and 15 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 6 and 10 is 30, and the LCM of 30 and 15 is 30 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 30 divisible by 6, 10 and 15?

Yes, and by definition it is the smallest positive integer that is: 30 ÷ 6, 30 ÷ 10 and 30 ÷ 15 all come out whole. Any other common multiple of 6, 10 and 15 is a multiple of 30.

See Also