LCM for 8, 9 and 15

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

What's the Least Common Multiple (LCM) of 8, 9 and 15?

Answer

LCM of 8, 9 and 15 is
360

(Three hundred sixty)

360 is the smallest positive integer that 8, 9 and 15 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 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 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 9: 3 × 3 (exponent form: 32)

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

Prime factor8915Highest power
223——23
3—32332
5——55

LCM = 23 × 32 × 5 = 360

Checking the LCM of 8, 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(8, 9) = (8 × 9) ÷ 1 = 72 ÷ 1 = 72

LCM(72, 15) = (72 × 15) ÷ 3 = 1,080 ÷ 3 = 360

LCM(8, 9, 15) = 360

The pairs may be taken in any order — 9 and 15 first, then 8 — and the answer is the same 360. 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 8, 9 and 15? (The answer is: 360). Enter the first number (e.g. '8'), 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
18972
28972
38972
48972
589360
68972
789504
88972
89972
8910360
8911792
891272
8913936
8914504
8915360
8916144
89171,224
891872
89191,368
8920360
8921504
8922792
89231,656
892472
89251,800
8926936
8927216
8928504
89292,088
8930360

FAQ

What's the Least Common Multiple (LCM) of 8, 9 and 15?

LCM of 8, 9 and 15 is 360

How to find the LCM of 8, 9 and 15 by prime factorization?

Take every prime that appears in 8, 9 and 15 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

Can you get the LCM of 8, 9 and 15 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 9 is 72, and the LCM of 72 and 15 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 360 divisible by 8, 9 and 15?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 8, 360 ÷ 9 and 360 ÷ 15 all come out whole. Any other common multiple of 8, 9 and 15 is a multiple of 360.

See Also