LCM for 8, 40 and 64

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

What's the Least Common Multiple (LCM) of 8, 40 and 64?

Answer

LCM of 8, 40 and 64 is
320

(Three hundred twenty)

320 is the smallest positive integer that 8, 40 and 64 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 40 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 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

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

Prime factor84064Highest power
223232626
5—5—5

LCM = 26 × 5 = 320

Checking the LCM of 8, 40 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, 40) = (8 × 40) ÷ 8 = 320 ÷ 8 = 40

LCM(40, 64) = (40 × 64) ÷ 8 = 2,560 ÷ 8 = 320

LCM(8, 40, 64) = 320

The pairs may be taken in any order — 40 and 64 first, then 8 — and the answer is the same 320. 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, 40 and 64? (The answer is: 320). Enter the first number (e.g. '8'), the second (e.g. '40') 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
840491,960
84050200
840512,040
84052520
840532,120
840541,080
84055440
84056280
840572,280
840581,160
840592,360
84060120
840612,440
840621,240
840632,520
84064320
84065520
840661,320
840672,680
84068680
840692,760
84070280
840712,840
84072360
840732,920
840741,480
84075600
84076760
840773,080
840781,560

FAQ

What's the Least Common Multiple (LCM) of 8, 40 and 64?

LCM of 8, 40 and 64 is 320

How to find the LCM of 8, 40 and 64 by prime factorization?

Take every prime that appears in 8, 40 and 64 to the highest power it reaches in any one of them and multiply: 2⁶ × 5 = 320.

Can you get the LCM of 8, 40 and 64 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 40 is 40, and the LCM of 40 and 64 is 320 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 320 divisible by 8, 40 and 64?

Yes, and by definition it is the smallest positive integer that is: 320 ÷ 8, 320 ÷ 40 and 320 ÷ 64 all come out whole. Any other common multiple of 8, 40 and 64 is a multiple of 320.

See Also