LCM for 8, 16 and 32

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

What's the Least Common Multiple (LCM) of 8, 16 and 32?

Answer

LCM of 8, 16 and 32 is
32

(Thirty-two)

32 is the smallest positive integer that 8, 16 and 32 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 16 and 32 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 32: 2 × 2 × 2 × 2 × 2 (exponent form: 25)

Prime factor81632Highest power
223242525

LCM = 25 = 32

Checking the LCM of 8, 16 and 32 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, 32) = (16 × 32) ÷ 16 = 512 ÷ 16 = 32

LCM(8, 16, 32) = 32

The pairs may be taken in any order — 16 and 32 first, then 8 — and the answer is the same 32. That is exactly why the two routes on this page agree.

Related Calculations

See Also

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 32? (The answer is: 32). Enter the first number (e.g. '8'), the second (e.g. '16') and the third (e.g. '32'), 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
81617272
81618144
81619304
8162080
81621336
81622176
81623368
8162448
81625400
81626208
81627432
81628112
81629464
81630240
81631496
8163232
81633528
81634272
81635560
81636144
81637592
81638304
81639624
8164080
81641656
81642336
81643688
81644176
81645720
81646368

FAQ

What's the Least Common Multiple (LCM) of 8, 16 and 32?

LCM of 8, 16 and 32 is 32

How to find the LCM of 8, 16 and 32 by prime factorization?

Take every prime that appears in 8, 16 and 32 to the highest power it reaches in any one of them and multiply: 2⁵ = 32.

Can you get the LCM of 8, 16 and 32 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 32 is 32 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 32 divisible by 8, 16 and 32?

Yes, and by definition it is the smallest positive integer that is: 32 ÷ 8, 32 ÷ 16 and 32 ÷ 32 all come out whole. Any other common multiple of 8, 16 and 32 is a multiple of 32.

See Also