LCM for 27, 36 and 45

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 27, 36 and 45?

Answer

LCM of 27, 36 and 45 is
540

(Five hundred forty)

540 is the smallest positive integer that 27, 36 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 27, 36 and 45 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 27: 3 × 3 × 3 (exponent form: 33)

All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

Prime factor273645Highest power
2—22—22
333323233
5——55

LCM = 22 × 33 × 5 = 540

Checking the LCM of 27, 36 and 45 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(27, 36) = (27 × 36) ÷ 9 = 972 ÷ 9 = 108

LCM(108, 45) = (108 × 45) ÷ 9 = 4,860 ÷ 9 = 540

LCM(27, 36, 45) = 540

The pairs may be taken in any order — 36 and 45 first, then 27 — and the answer is the same 540. 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 27, 36 and 45? (The answer is: 540). Enter the first number (e.g. '27'), the second (e.g. '36') and the third (e.g. '45'), 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
273036540
2731363,348
273236864
2733361,188
2734361,836
2735363,780
273636108
2736373,996
2736382,052
2736391,404
2736401,080
2736414,428
273642756
2736434,644
2736441,188
273645540
2736462,484
2736475,076
273648432
2736495,292
2736502,700
2736511,836
2736521,404
2736535,724
273654108
2736555,940
2736561,512
2736572,052
2736583,132
2736596,372

FAQ

What's the Least Common Multiple (LCM) of 27, 36 and 45?

LCM of 27, 36 and 45 is 540

How to find the LCM of 27, 36 and 45 by prime factorization?

Take every prime that appears in 27, 36 and 45 to the highest power it reaches in any one of them and multiply: 2² × 3³ × 5 = 540.

Can you get the LCM of 27, 36 and 45 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 27 and 36 is 108, and the LCM of 108 and 45 is 540 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 540 divisible by 27, 36 and 45?

Yes, and by definition it is the smallest positive integer that is: 540 ÷ 27, 540 ÷ 36 and 540 ÷ 45 all come out whole. Any other common multiple of 27, 36 and 45 is a multiple of 540.

See Also