LCM for 32, 48 and 64

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 32, 48 and 64?

Answer

LCM of 32, 48 and 64 is
192

(One hundred ninety-two)

192 is the smallest positive integer that 32, 48 and 64 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 32, 48 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 32: 2 × 2 × 2 × 2 × 2 (exponent form: 25)

All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

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

Prime factor324864Highest power
225242626
3—3—3

LCM = 26 × 3 = 192

Checking the LCM of 32, 48 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(32, 48) = (32 × 48) ÷ 16 = 1,536 ÷ 16 = 96

LCM(96, 64) = (96 × 64) ÷ 32 = 6,144 ÷ 32 = 192

LCM(32, 48, 64) = 192

The pairs may be taken in any order — 48 and 64 first, then 32 — and the answer is the same 192. 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 32, 48 and 64? (The answer is: 192). Enter the first number (e.g. '32'), the second (e.g. '48') 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
3248494,704
3248502,400
3248511,632
3248521,248
3248535,088
324854864
3248555,280
324856672
3248571,824
3248582,784
3248595,664
324860480
3248615,856
3248622,976
3248632,016
324864192
3248656,240
3248661,056
3248676,432
3248681,632
3248692,208
3248703,360
3248716,816
324872288
3248737,008
3248743,552
3248752,400
3248761,824
3248777,392
3248781,248

FAQ

What's the Least Common Multiple (LCM) of 32, 48 and 64?

LCM of 32, 48 and 64 is 192

How to find the LCM of 32, 48 and 64 by prime factorization?

Take every prime that appears in 32, 48 and 64 to the highest power it reaches in any one of them and multiply: 2⁶ × 3 = 192.

Can you get the LCM of 32, 48 and 64 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 32 and 48 is 96, and the LCM of 96 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 32, 48 and 64?

Yes, and by definition it is the smallest positive integer that is: 192 ÷ 32, 192 ÷ 48 and 192 ÷ 64 all come out whole. Any other common multiple of 32, 48 and 64 is a multiple of 192.

See Also