LCM for 8, 16 and 24

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

What's the Least Common Multiple (LCM) of 8, 16 and 24?

Answer

LCM of 8, 16 and 24 is
48

(Forty-eight)

48 is the smallest positive integer that 8, 16 and 24 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 16 and 24 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

Prime factor81624Highest power
223242324
3——33

LCM = 24 × 3 = 48

Checking the LCM of 8, 16 and 24 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, 16) = (8 × 16) ÷ 8 = 128 ÷ 8 = 16

LCM(16, 24) = (16 × 24) ÷ 8 = 384 ÷ 8 = 48

LCM(8, 16, 24) = 48

The pairs may be taken in any order — 16 and 24 first, then 8 — and the answer is the same 48. That is exactly why the two routes on this page agree.

Related Calculations

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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, 16 and 24? (The answer is: 48). Enter the first number (e.g. '8'), the second (e.g. '16') and the third (e.g. '24'), 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
8916144
8101680
81116176
8121648
81316208
81416112
81516240
8161616
81617272
81618144
81619304
8162080
81621336
81622176
81623368
8162448
81625400
81626208
81627432
81628112
81629464
81630240
81631496
8163232
81633528
81634272
81635560
81636144
81637592
81638304

FAQ

What's the Least Common Multiple (LCM) of 8, 16 and 24?

LCM of 8, 16 and 24 is 48

How to find the LCM of 8, 16 and 24 by prime factorization?

Take every prime that appears in 8, 16 and 24 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 = 48.

Can you get the LCM of 8, 16 and 24 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 16 is 16, and the LCM of 16 and 24 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, 16 and 24?

Yes, and by definition it is the smallest positive integer that is: 48 ÷ 8, 48 ÷ 16 and 48 ÷ 24 all come out whole. Any other common multiple of 8, 16 and 24 is a multiple of 48.

See Also