LCM for 8, 56 and 64

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What's the Least Common Multiple (LCM) of 8, 56 and 64?

Answer

LCM of 8, 56 and 64 is
448

First common multiples: 448; 896; 1,344; …

448 is divisible by all three: 448 ÷ 8 = 56, 448 ÷ 56 = 8, 448 ÷ 64 = 7 — and 56, 8 and 7 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/8 by 56 and of y/56 by 8 and of z/64 by 7.

8 = 23

56 = 23 × 7

64 = 26

Prime85664Highest power
223232626
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 = 26 × 7 = 448

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LCM Table

1st2nd3rdLCM
84956392
850561,400
851562,856
85256728
853562,968
854561,512
855563,080
8565656
856573,192
856581,624
856593,304
85660840
856613,416
856621,736
85663504
85664448
856653,640
856661,848
856673,752
85668952
856693,864
85670280
856713,976
85672504
856734,088
856742,072
856754,200
856761,064
85677616
856782,184

FAQ

What's the Least Common Multiple (LCM) of 8, 56 and 64?

LCM of 8, 56 and 64 is 448

How to find the LCM of 8, 56 and 64 by prime factorization?

Take every prime that appears in 8, 56 and 64 to the highest power it reaches in any one of them and multiply: 2⁶ × 7 = 448.

Can you get the LCM of 8, 56 and 64 two numbers at a time?

Yes. The LCM of 8 and 56 is 56, and the LCM of 56 and 64 is 448 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 448 divisible by 8, 56 and 64?

Yes, and by definition it is the smallest positive integer that is: 448 ÷ 8, 448 ÷ 56 and 448 ÷ 64 all come out whole. Any other common multiple of 8, 56 and 64 is a multiple of 448.

See Also