LCM for 18, 24 and 30

"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 30?

Answer

LCM of 18, 24 and 30 is
360

(Three hundred sixty)

360 is the smallest positive integer that 18, 24 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 18, 24 and 30 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

Prime factor182430Highest power
2223223
3323332
5——55

LCM = 23 × 32 × 5 = 360

Checking the LCM of 18, 24 and 30 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, 30) = (72 × 30) ÷ 6 = 2,160 ÷ 6 = 360

LCM(18, 24, 30) = 360

The pairs may be taken in any order — 24 and 30 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 30? (The answer is: 360). Enter the first number (e.g. '18'), the second (e.g. '24') and the third (e.g. '30'), 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
151824360
161824144
1718241,224
18182472
1819241,368
182024360
182124504
182224792
1823241,656
18242472
1824251,800
182426936
182427216
182428504
1824292,088
182430360
1824312,232
182432288
182433792
1824341,224
1824352,520
18243672
1824372,664
1824381,368
182439936
182440360
1824412,952
182442504
1824433,096
182444792

FAQ

What's the Least Common Multiple (LCM) of 18, 24 and 30?

LCM of 18, 24 and 30 is 360

How to find the LCM of 18, 24 and 30 by prime factorization?

Take every prime that appears in 18, 24 and 30 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 30 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 30 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 30?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 18, 360 ÷ 24 and 360 ÷ 30 all come out whole. Any other common multiple of 18, 24 and 30 is a multiple of 360.

See Also