LCM for 8, 56 and 64

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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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

(Four hundred forty-eight)

448 is the smallest positive integer that 8, 56 and 64 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 56 and 64 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 56: 2 × 2 × 2 × 7 (exponent form: 23 × 7)

All Prime Factors of 64: 2 × 2 × 2 × 2 × 2 × 2 (exponent form: 26)

Prime factor85664Highest power
223232626
7—7—7

LCM = 26 × 7 = 448

Checking the LCM of 8, 56 and 64 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(8, 56) = (8 × 56) ÷ 8 = 448 ÷ 8 = 56

LCM(56, 64) = (56 × 64) ÷ 8 = 3,584 ÷ 8 = 448

LCM(8, 56, 64) = 448

The pairs may be taken in any order — 56 and 64 first, then 8 — and the answer is the same 448. That is exactly why the two routes on this page agree.

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About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 8, 56 and 64? (The answer is: 448). Enter the first number (e.g. '8'), the second (e.g. '56') and the third (e.g. '64'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
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, and it is the check this page prints. 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