LCM for 5, 7 and 8

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What's the Least Common Multiple (LCM) of 5, 7 and 8?

Answer

LCM of 5, 7 and 8 is
280

First common multiples: 280, 560, 840, …

280 is divisible by all three: 280 ÷ 5 = 56, 280 ÷ 7 = 40, 280 ÷ 8 = 35 — and 56, 40 and 35 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 56 and of y/7 by 40 and of z/8 by 35.

5 — prime

7 — prime

8 = 23

Prime578Highest power
2——2323
55——5
7—7—7

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

LCM = 23 × 5 × 7 = 280

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LCM Table

1st2nd3rdLCM
15735
25770
357105
457140
55735
567210
57735
578280
579315
571070
5711385
5712420
5713455
571470
5715105
5716560
5717595
5718630
5719665
5720140
5721105
5722770
5723805
5724840
5725175
5726910
5727945
5728140
57291,015
5730210

FAQ

What's the Least Common Multiple (LCM) of 5, 7 and 8?

LCM of 5, 7 and 8 is 280

How to find the LCM of 5, 7 and 8 by prime factorization?

Take every prime that appears in 5, 7 and 8 to the highest power it reaches in any one of them and multiply: 2³ × 5 × 7 = 280.

Can you get the LCM of 5, 7 and 8 two numbers at a time?

Yes. The LCM of 5 and 7 is 35, and the LCM of 35 and 8 is 280 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 280 divisible by 5, 7 and 8?

Yes, and by definition it is the smallest positive integer that is: 280 ÷ 5, 280 ÷ 7 and 280 ÷ 8 all come out whole. Any other common multiple of 5, 7 and 8 is a multiple of 280.

See Also