LCM for 5, 8 and 9

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What's the Least Common Multiple (LCM) of 5, 8 and 9?

Answer

LCM of 5, 8 and 9 is
360

First common multiples: 360; 720; 1,080; …

360 is divisible by all three: 360 ÷ 5 = 72, 360 ÷ 8 = 45, 360 ÷ 9 = 40 — and 72, 45 and 40 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/5 by 72 and of y/8 by 45 and of z/9 by 40.

5 — prime

8 = 23

9 = 32

Prime589Highest power
2—23—23
3——3232
55——5

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

LCM = 23 × 32 × 5 = 360

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LCM Table

1st2nd3rdLCM
15840
25840
358120
45840
55840
568120
578280
58840
589360
581040
5811440
5812120
5813520
5814280
5815120
581680
5817680
5818360
5819760
582040
5821840
5822440
5823920
5824120
5825200
5826520
58271,080
5828280
58291,160
5830120

FAQ

What's the Least Common Multiple (LCM) of 5, 8 and 9?

LCM of 5, 8 and 9 is 360

How to find the LCM of 5, 8 and 9 by prime factorization?

Take every prime that appears in 5, 8 and 9 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

Can you get the LCM of 5, 8 and 9 two numbers at a time?

Yes. The LCM of 5 and 8 is 40, and the LCM of 40 and 9 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 360 divisible by 5, 8 and 9?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 5, 360 ÷ 8 and 360 ÷ 9 all come out whole. Any other common multiple of 5, 8 and 9 is a multiple of 360.

See Also