LCM for 27, 36 and 45

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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

First common multiples: 540; 1,080; 1,620; …

540 is divisible by all three: 540 ÷ 27 = 20, 540 ÷ 36 = 15, 540 ÷ 45 = 12 — and 20, 15 and 12 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/27 by 20 and of y/36 by 15 and of z/45 by 12.

27 = 33

36 = 22 × 32

45 = 32 × 5

Prime273645Highest power
2—22—22
333323233
5——55

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 22 × 33 × 5 = 540

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LCM Table

1st2nd3rdLCM
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. 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