LCM for 6, 18 and 45

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What's the Least Common Multiple (LCM) of 6, 18 and 45?

Answer

LCM of 6, 18 and 45 is
90

First common multiples: 90, 180, 270, …

90 is divisible by all three: 90 ÷ 6 = 15, 90 ÷ 18 = 5, 90 ÷ 45 = 2 — and 15, 5 and 2 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/6 by 15 and of y/18 by 5 and of z/45 by 2.

6 = 2 × 3

18 = 2 × 32

45 = 32 × 5

Prime61845Highest power
222—2
33323232
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 × 32 × 5 = 90

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LCM Table

1st2nd3rdLCM
6183090
61831558
61832288
61833198
61834306
61835630
6183636
61837666
61838342
61839234
61840360
61841738
61842126
61843774
61844396
6184590
61846414
61847846
61848144
61849882
61850450
61851306
61852468
61853954
6185454
61855990
61856504
61857342
61858522
618591,062

FAQ

What's the Least Common Multiple (LCM) of 6, 18 and 45?

LCM of 6, 18 and 45 is 90

How to find the LCM of 6, 18 and 45 by prime factorization?

Take every prime that appears in 6, 18 and 45 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

Can you get the LCM of 6, 18 and 45 two numbers at a time?

Yes. The LCM of 6 and 18 is 18, and the LCM of 18 and 45 is 90 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 90 divisible by 6, 18 and 45?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 6, 90 ÷ 18 and 90 ÷ 45 all come out whole. Any other common multiple of 6, 18 and 45 is a multiple of 90.

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