LCM for 18, 27 and 45

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What's the Least Common Multiple (LCM) of 18, 27 and 45?

Answer

LCM of 18, 27 and 45 is
270

First common multiples: 270, 540, 810, …

270 is divisible by all three: 270 ÷ 18 = 15, 270 ÷ 27 = 10, 270 ÷ 45 = 6 — and 15, 10 and 6 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/18 by 15 and of y/27 by 10 and of z/45 by 6.

18 = 2 × 32

27 = 33

45 = 32 × 5

Prime182745Highest power
22——2
332333233
5——55

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

LCM = 2 × 33 × 5 = 270

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LCM Table

1st2nd3rdLCM
182730270
1827311,674
182732864
182733594
182734918
1827351,890
182736108
1827371,998
1827381,026
182739702
1827401,080
1827412,214
182742378
1827432,322
1827441,188
182745270
1827461,242
1827472,538
182748432
1827492,646
1827501,350
182751918
1827521,404
1827532,862
18275454
1827552,970
1827561,512
1827571,026
1827581,566
1827593,186

FAQ

What's the Least Common Multiple (LCM) of 18, 27 and 45?

LCM of 18, 27 and 45 is 270

How to find the LCM of 18, 27 and 45 by prime factorization?

Take every prime that appears in 18, 27 and 45 to the highest power it reaches in any one of them and multiply: 2 × 3³ × 5 = 270.

Can you get the LCM of 18, 27 and 45 two numbers at a time?

Yes. The LCM of 18 and 27 is 54, and the LCM of 54 and 45 is 270 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 270 divisible by 18, 27 and 45?

Yes, and by definition it is the smallest positive integer that is: 270 ÷ 18, 270 ÷ 27 and 270 ÷ 45 all come out whole. Any other common multiple of 18, 27 and 45 is a multiple of 270.

See Also