LCM for 8, 24 and 64

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

What's the Least Common Multiple (LCM) of 8, 24 and 64?

Answer

LCM of 8, 24 and 64 is
192

(One hundred ninety-two)

192 is the smallest positive integer that 8, 24 and 64 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 24 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 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

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

Prime factor82464Highest power
223232626
3—3—3

LCM = 26 × 3 = 192

Checking the LCM of 8, 24 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, 24) = (8 × 24) ÷ 8 = 192 ÷ 8 = 24

LCM(24, 64) = (24 × 64) ÷ 8 = 1,536 ÷ 8 = 192

LCM(8, 24, 64) = 192

The pairs may be taken in any order — 24 and 64 first, then 8 — and the answer is the same 192. 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, 24 and 64? (The answer is: 192). Enter the first number (e.g. '8'), the second (e.g. '24') 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
824491,176
82450600
82451408
82452312
824531,272
82454216
824551,320
82456168
82457456
82458696
824591,416
82460120
824611,464
82462744
82463504
82464192
824651,560
82466264
824671,608
82468408
82469552
82470840
824711,704
8247272
824731,752
82474888
82475600
82476456
824771,848
82478312

FAQ

What's the Least Common Multiple (LCM) of 8, 24 and 64?

LCM of 8, 24 and 64 is 192

How to find the LCM of 8, 24 and 64 by prime factorization?

Take every prime that appears in 8, 24 and 64 to the highest power it reaches in any one of them and multiply: 2⁶ × 3 = 192.

Can you get the LCM of 8, 24 and 64 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 24 is 24, and the LCM of 24 and 64 is 192 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 192 divisible by 8, 24 and 64?

Yes, and by definition it is the smallest positive integer that is: 192 ÷ 8, 192 ÷ 24 and 192 ÷ 64 all come out whole. Any other common multiple of 8, 24 and 64 is a multiple of 192.

See Also