LCM for 16, 40 and 56

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What's the Least Common Multiple (LCM) of 16, 40 and 56?

Answer

LCM of 16, 40 and 56 is
560

First common multiples: 560; 1,120; 1,680; …

560 is divisible by all three: 560 ÷ 16 = 35, 560 ÷ 40 = 14, 560 ÷ 56 = 10 — and 35, 14 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/16 by 35 and of y/40 by 14 and of z/56 by 10.

16 = 24

40 = 23 × 5

56 = 23 × 7

Prime164056Highest power
224232324
5—5—5
7——77

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

LCM = 24 × 5 × 7 = 560

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LCM Table

1st2nd3rdLCM
1640413,280
1640421,680
1640433,440
164044880
164045720
1640461,840
1640473,760
164048240
1640493,920
164050400
1640514,080
1640521,040
1640534,240
1640542,160
164055880
164056560
1640574,560
1640582,320
1640594,720
164060240
1640614,880
1640622,480
1640635,040
164064320
1640651,040
1640662,640
1640675,360
1640681,360
1640695,520
164070560

FAQ

What's the Least Common Multiple (LCM) of 16, 40 and 56?

LCM of 16, 40 and 56 is 560

How to find the LCM of 16, 40 and 56 by prime factorization?

Take every prime that appears in 16, 40 and 56 to the highest power it reaches in any one of them and multiply: 2⁴ × 5 × 7 = 560.

Can you get the LCM of 16, 40 and 56 two numbers at a time?

Yes. The LCM of 16 and 40 is 80, and the LCM of 80 and 56 is 560 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 560 divisible by 16, 40 and 56?

Yes, and by definition it is the smallest positive integer that is: 560 ÷ 16, 560 ÷ 40 and 560 ÷ 56 all come out whole. Any other common multiple of 16, 40 and 56 is a multiple of 560.

See Also