LCM for 4, 5 and 9

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What's the Least Common Multiple (LCM) of 4, 5 and 9?

Answer

LCM of 4, 5 and 9 is
180

First common multiples: 180, 360, 540, …

180 is divisible by all three: 180 ÷ 4 = 45, 180 ÷ 5 = 36, 180 ÷ 9 = 20 — and 45, 36 and 20 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/5 by 36 and of z/9 by 20.

4 = 22

5 — prime

9 = 32

Prime459Highest power
222——22
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
14520
24520
34560
44520
45520
45660
457140
45840
459180
451020
4511220
451260
4513260
4514140
451560
451680
4517340
4518180
4519380
452020
4521420
4522220
4523460
4524120
4525100
4526260
4527540
4528140
4529580
453060

FAQ

What's the Least Common Multiple (LCM) of 4, 5 and 9?

LCM of 4, 5 and 9 is 180

How to find the LCM of 4, 5 and 9 by prime factorization?

Take every prime that appears in 4, 5 and 9 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 4, 5 and 9 two numbers at a time?

Yes. The LCM of 4 and 5 is 20, and the LCM of 20 and 9 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, 5 and 9?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 4, 180 ÷ 5 and 180 ÷ 9 all come out whole. Any other common multiple of 4, 5 and 9 is a multiple of 180.

See Also