LCM for 18, 24 and 60

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 18, 24 and 60?

Answer

LCM of 18, 24 and 60 is
360

(Three hundred sixty)

360 is the smallest positive integer that 18, 24 and 60 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 18, 24 and 60 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

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

All Prime Factors of 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

Prime factor182460Highest power
22232223
3323332
5——55

LCM = 23 × 32 × 5 = 360

Checking the LCM of 18, 24 and 60 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(18, 24) = (18 × 24) ÷ 6 = 432 ÷ 6 = 72

LCM(72, 60) = (72 × 60) ÷ 12 = 4,320 ÷ 12 = 360

LCM(18, 24, 60) = 360

The pairs may be taken in any order — 24 and 60 first, then 18 — and the answer is the same 360. 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 18, 24 and 60? (The answer is: 360). Enter the first number (e.g. '18'), the second (e.g. '24') and the third (e.g. '60'), 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
182445360
1824461,656
1824473,384
182448144
1824493,528
1824501,800
1824511,224
182452936
1824533,816
182454216
1824553,960
182456504
1824571,368
1824582,088
1824594,248
182460360
1824614,392
1824622,232
182463504
182464576
1824654,680
182466792
1824674,824
1824681,224
1824691,656
1824702,520
1824715,112
18247272
1824735,256
1824742,664

FAQ

What's the Least Common Multiple (LCM) of 18, 24 and 60?

LCM of 18, 24 and 60 is 360

How to find the LCM of 18, 24 and 60 by prime factorization?

Take every prime that appears in 18, 24 and 60 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

Can you get the LCM of 18, 24 and 60 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 18 and 24 is 72, and the LCM of 72 and 60 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 18, 24 and 60?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 18, 360 ÷ 24 and 360 ÷ 60 all come out whole. Any other common multiple of 18, 24 and 60 is a multiple of 360.

See Also