LCM for 4, 10 and 18

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What's the Least Common Multiple (LCM) of 4, 10 and 18?

Answer

LCM of 4, 10 and 18 is
180

First common multiples: 180, 360, 540, …

180 is divisible by all three: 180 ÷ 4 = 45, 180 ÷ 10 = 18, 180 ÷ 18 = 10 — and 45, 18 and 10 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/4 by 45 and of y/10 by 18 and of z/18 by 10.

4 = 22

10 = 2 × 5

18 = 2 × 32

Prime41018Highest power
2222222
3——3232
5—5—5

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

LCM = 22 × 32 × 5 = 180

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LCM Table

1st2nd3rdLCM
341060
441020
451020
461060
4710140
481040
4910180
4101020
41011220
4101260
41013260
41014140
4101560
4101680
41017340
41018180
41019380
4102020
41021420
41022220
41023460
41024120
41025100
41026260
41027540
41028140
41029580
4103060
41031620
41032160

FAQ

What's the Least Common Multiple (LCM) of 4, 10 and 18?

LCM of 4, 10 and 18 is 180

How to find the LCM of 4, 10 and 18 by prime factorization?

Take every prime that appears in 4, 10 and 18 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 4, 10 and 18 two numbers at a time?

Yes. The LCM of 4 and 10 is 20, and the LCM of 20 and 18 is 180 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 180 divisible by 4, 10 and 18?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 4, 180 ÷ 10 and 180 ÷ 18 all come out whole. Any other common multiple of 4, 10 and 18 is a multiple of 180.

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