LCM for 8, 24 and 48

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 8, 24 and 48?

Answer

LCM of 8, 24 and 48 is
48

(Forty-eight)

48 is the smallest positive integer that 8, 24 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 24 and 48 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 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

Prime factor82448Highest power
223232424
3—333

LCM = 24 × 3 = 48

Checking the LCM of 8, 24 and 48 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, 48) = (24 × 48) ÷ 24 = 1,152 ÷ 24 = 48

LCM(8, 24, 48) = 48

The pairs may be taken in any order — 24 and 48 first, then 8 — and the answer is the same 48. 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 48? (The answer is: 48). Enter the first number (e.g. '8'), the second (e.g. '24') and the third (e.g. '48'), 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
82433264
82434408
82435840
8243672
82437888
82438456
82439312
82440120
82441984
82442168
824431,032
82444264
82445360
82446552
824471,128
8244848
824491,176
82450600
82451408
82452312
824531,272
82454216
824551,320
82456168
82457456
82458696
824591,416
82460120
824611,464
82462744

FAQ

What's the Least Common Multiple (LCM) of 8, 24 and 48?

LCM of 8, 24 and 48 is 48

How to find the LCM of 8, 24 and 48 by prime factorization?

Take every prime that appears in 8, 24 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 = 48.

Can you get the LCM of 8, 24 and 48 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 48 is 48 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 48 divisible by 8, 24 and 48?

Yes, and by definition it is the smallest positive integer that is: 48 ÷ 8, 48 ÷ 24 and 48 ÷ 48 all come out whole. Any other common multiple of 8, 24 and 48 is a multiple of 48.

See Also