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The lcm of 65 and 32 is the smallest positive integer that divides the numbers 65 and 32 without a remainder. Spelled out, it is the least common multiple of 65 and 32. Here you can find the result for 65 and 32, along with a total of three methods for computing it.
2080
What is the Least Common Multiple of 65 and 32?
If you just want to know what is the least common multiple of 65 and 32, it is 2080. Usually, this is written as
The lcm of 65 and 32 can be obtained like this:
- The multiples of 65 are … , 2015, 2080, 2145, ….
- The multiples of 32 are …, 2048, 2080, 2112, …
- The common multiples of 65 and 32 are n x 2080, intersecting the two sets above,
. - In the intersection multiples of 65 ∩ multiples of 32 the least positive element is 2080.
- Therefore, the least common multiple of 65 and 32 is 2080.
Taking the above into account you also know how to find all the common multiples of 65 and 32, not just the smallest. In the next section we show you how to calculate the lcm of sixty-five and thirty-two by means of two more methods.
How to find the LCM of 65 and 32
The least common multiple of 65 and 32 can be computed by using the greatest common factor aka gcf of 65 and 32. This is the easiest approach:
Alternatively, the lcm of 65 and 32 can be found using the prime factorization of 65 and 32:
- The prime factorization of 65 is: 5 x 13
- The prime factorization of 32 is: 2 x 2 x 2 x 2 x 2
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(65,65) = 2080
In any case, the easiest way to compute the result for two numbers like 65 and 32 is by using our calculator above. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 65,322,2. Push the button only to start over.
Similar searched terms on our site also include:
In the next paragraph we explain how the mathematical concept can be employed.
Keep reading – it’s really interesting.
Use of Least Common Multiple of 65 and 32
What is the least common multiple of 65 and 32 used for? Answer: It is helpful for adding and subtracting fractions like 1/65 and 1/32. Just multiply the dividends and divisors by 32 and 65, respectively, such that the divisors have the value of 2080, the lcm of 65 and 32.
Next, we shed a light on the mathematical properties.
Properties of LCM of 65 and 32
The most important properties of the lcm(65,32) are:
- Commutative property: lcm(65,32) = lcm(32,65)
- Associative property: lcm(65,32,n) = lcm(lcm(32,65),n)
The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.
Summary
Note that you can find the least common multiple of many integer pairs including sixty-five / thirty-two by using the search form in the sidebar of this page.
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– Article written by Mark, last updated on August 8th, 2023