LCM for 6, 9 and 15

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

What's the Least Common Multiple (LCM) of 6, 9 and 15?

Answer

LCM of 6, 9 and 15 is
90

(Ninety)

90 is the smallest positive integer that 6, 9 and 15 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 6, 9 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 9: 3 × 3 (exponent form: 32)

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

Prime factor6915Highest power
22——2
3332332
5——55

LCM = 2 × 32 × 5 = 90

Checking the LCM of 6, 9 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, 9) = (6 × 9) ÷ 3 = 54 ÷ 3 = 18

LCM(18, 15) = (18 × 15) ÷ 3 = 270 ÷ 3 = 90

LCM(6, 9, 15) = 90

The pairs may be taken in any order — 9 and 15 first, then 6 — and the answer is the same 90. 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, 9 and 15? (The answer is: 90). Enter the first number (e.g. '6'), the second (e.g. '9') 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
16918
26918
36918
46936
56990
66918
679126
68972
69918
691090
6911198
691236
6913234
6914126
691590
6916144
6917306
691818
6919342
6920180
6921126
6922198
6923414
692472
6925450
6926234
692754
6928252
6929522
693090

FAQ

What's the Least Common Multiple (LCM) of 6, 9 and 15?

LCM of 6, 9 and 15 is 90

How to find the LCM of 6, 9 and 15 by prime factorization?

Take every prime that appears in 6, 9 and 15 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

Can you get the LCM of 6, 9 and 15 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 6 and 9 is 18, and the LCM of 18 and 15 is 90 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 90 divisible by 6, 9 and 15?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 6, 90 ÷ 9 and 90 ÷ 15 all come out whole. Any other common multiple of 6, 9 and 15 is a multiple of 90.

See Also