LCM for 8, 12 and 15

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

What's the Least Common Multiple (LCM) of 8, 12 and 15?

Answer

LCM of 8, 12 and 15 is
120

(One hundred twenty)

120 is the smallest positive integer that 8, 12 and 15 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 12 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

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

Prime factor81215Highest power
22322—23
3—333
5——55

LCM = 23 × 3 × 5 = 120

Checking the LCM of 8, 12 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, 12) = (8 × 12) ÷ 4 = 96 ÷ 4 = 24

LCM(24, 15) = (24 × 15) ÷ 3 = 360 ÷ 3 = 120

LCM(8, 12, 15) = 120

The pairs may be taken in any order — 12 and 15 first, then 8 — and the answer is the same 120. That is exactly why the two routes on this page agree.

Related Calculations

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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 8, 12 and 15? (The answer is: 120). Enter the first number (e.g. '8'), the second (e.g. '12') 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
181224
281224
381224
481224
5812120
681224
7812168
881224
891272
81012120
81112264
8121224
81213312
81214168
81215120
8121648
81217408
8121872
81219456
81220120
81221168
81222264
81223552
8122424
81225600
81226312
81227216
81228168
81229696
81230120

FAQ

What's the Least Common Multiple (LCM) of 8, 12 and 15?

LCM of 8, 12 and 15 is 120

How to find the LCM of 8, 12 and 15 by prime factorization?

Take every prime that appears in 8, 12 and 15 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 8, 12 and 15 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 12 is 24, and the LCM of 24 and 15 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 8, 12 and 15?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 8, 120 ÷ 12 and 120 ÷ 15 all come out whole. Any other common multiple of 8, 12 and 15 is a multiple of 120.

See Also