LCM for 5, 8 and 12

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What's the Least Common Multiple (LCM) of 5, 8 and 12?

Answer

LCM of 5, 8 and 12 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 5 = 24, 120 ÷ 8 = 15, 120 ÷ 12 = 10 — and 24, 15 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/5 by 24 and of y/8 by 15 and of z/12 by 10.

5 — prime

8 = 23

12 = 22 × 3

Prime5812Highest power
2—232223
3——33
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 × 3 × 5 = 120

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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 12?

LCM of 5, 8 and 12 is 120

How to find the LCM of 5, 8 and 12 by prime factorization?

Take every prime that appears in 5, 8 and 12 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 5, 8 and 12 two numbers at a time?

Yes. The LCM of 5 and 8 is 40, and the LCM of 40 and 12 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 5, 8 and 12?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 5, 120 ÷ 8 and 120 ÷ 12 all come out whole. Any other common multiple of 5, 8 and 12 is a multiple of 120.

See Also