LCM for 8, 24 and 36

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

What's the Least Common Multiple (LCM) of 8, 24 and 36?

Answer

LCM of 8, 24 and 36 is
72

(Seventy-two)

72 is the smallest positive integer that 8, 24 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 24 and 36 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 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

Prime factor82436Highest power
223232223
3—33232

LCM = 23 × 32 = 72

Checking the LCM of 8, 24 and 36 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, 36) = (24 × 36) ÷ 12 = 864 ÷ 12 = 72

LCM(8, 24, 36) = 72

The pairs may be taken in any order — 24 and 36 first, then 8 — and the answer is the same 72. 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 36? (The answer is: 72). Enter the first number (e.g. '8'), the second (e.g. '24') and the third (e.g. '36'), 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
82124168
82224264
82324552
8242424
82425600
82426312
82427216
82428168
82429696
82430120
82431744
8243296
82433264
82434408
82435840
8243672
82437888
82438456
82439312
82440120
82441984
82442168
824431,032
82444264
82445360
82446552
824471,128
8244848
824491,176
82450600

FAQ

What's the Least Common Multiple (LCM) of 8, 24 and 36?

LCM of 8, 24 and 36 is 72

How to find the LCM of 8, 24 and 36 by prime factorization?

Take every prime that appears in 8, 24 and 36 to the highest power it reaches in any one of them and multiply: 2³ × 3² = 72.

Can you get the LCM of 8, 24 and 36 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 36 is 72 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 72 divisible by 8, 24 and 36?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 8, 72 ÷ 24 and 72 ÷ 36 all come out whole. Any other common multiple of 8, 24 and 36 is a multiple of 72.

See Also