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The lcm of 39 and 53 is the smallest positive integer that divides the numbers 39 and 53 without a remainder. Spelled out, it is the least common multiple of 39 and 53. Here you can find the result for 39 and 53, along with a total of three methods for computing it.
2067
What is the Least Common Multiple of 39 and 53?
If you just want to know what is the least common multiple of 39 and 53, it is 2067. Usually, this is written as
The lcm of 39 and 53 can be obtained like this:
- The multiples of 39 are … , 2028, 2067, 2106, ….
- The multiples of 53 are …, 2014, 2067, 2120, …
- The common multiples of 39 and 53 are n x 2067, intersecting the two sets above,
. - In the intersection multiples of 39 ∩ multiples of 53 the least positive element is 2067.
- Therefore, the least common multiple of 39 and 53 is 2067.
Taking the above into account you also know how to find all the common multiples of 39 and 53, not just the smallest. In the next section we show you how to calculate the lcm of thirty-nine and fifty-three by means of two more methods.
How to find the LCM of 39 and 53
The least common multiple of 39 and 53 can be computed by using the greatest common factor aka gcf of 39 and 53. This is the easiest approach:
Alternatively, the lcm of 39 and 53 can be found using the prime factorization of 39 and 53:
- The prime factorization of 39 is: 3 x 13
- The prime factorization of 53 is: 53
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(39,39) = 2067
In any case, the easiest way to compute the result for two numbers like 39 and 53 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 39,532,2. 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 39 and 53
What is the least common multiple of 39 and 53 used for? Answer: It is helpful for adding and subtracting fractions like 1/39 and 1/53. Just multiply the dividends and divisors by 53 and 39, respectively, such that the divisors have the value of 2067, the lcm of 39 and 53.
Next, we shed a light on the mathematical properties.
Properties of LCM of 39 and 53
The most important properties of the lcm(39,53) are:
- Commutative property: lcm(39,53) = lcm(53,39)
- Associative property: lcm(39,53,n) = lcm(lcm(53,39),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 thirty-nine / fifty-three 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