LCM for 10, 15 and 24

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

What's the Least Common Multiple (LCM) of 10, 15 and 24?

Answer

LCM of 10, 15 and 24 is
120

(One hundred twenty)

120 is the smallest positive integer that 10, 15 and 24 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 15 and 24 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 10: 2 × 5 (exponent form: 2 × 5)

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

All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

Prime factor101524Highest power
22—2323
3—333
555—5

LCM = 23 × 3 × 5 = 120

Checking the LCM of 10, 15 and 24 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(10, 15) = (10 × 15) ÷ 5 = 150 ÷ 5 = 30

LCM(30, 24) = (30 × 24) ÷ 6 = 720 ÷ 6 = 120

LCM(10, 15, 24) = 120

The pairs may be taken in any order — 15 and 24 first, then 10 — and the answer is the same 120. That is exactly why the two routes on this page agree.

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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 10, 15 and 24? (The answer is: 120). Enter the first number (e.g. '10'), the second (e.g. '15') and the third (e.g. '24'), 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
9101590
10101530
101115330
10121560
101315390
101415210
10151530
101516240
101517510
10151890
101519570
10152060
101521210
101522330
101523690
101524120
101525150
101526390
101527270
101528420
101529870
10153030
101531930
101532480
101533330
101534510
101535210
101536180
1015371,110
101538570

FAQ

What's the Least Common Multiple (LCM) of 10, 15 and 24?

LCM of 10, 15 and 24 is 120

How to find the LCM of 10, 15 and 24 by prime factorization?

Take every prime that appears in 10, 15 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 10, 15 and 24 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 10 and 15 is 30, and the LCM of 30 and 24 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 10, 15 and 24?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 10, 120 ÷ 15 and 120 ÷ 24 all come out whole. Any other common multiple of 10, 15 and 24 is a multiple of 120.

See Also