Home » Least Common Multiple » LCM of 25 and 13

LCM of 25 and 13

The lcm of 25 and 13 is the smallest positive integer that divides the numbers 25 and 13 without a remainder. Spelled out, it is the least common multiple of 25 and 13. Here you can find the result for 25 and 13, along with a total of three methods for computing it.


325

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 25 and 13, but also that of three or more integers including twenty-five and thirteen for example. Keep reading to learn everything about the lcm (25,13) and the terms related to it.

What is the Least Common Multiple of 25 and 13?

If you just want to know what is the least common multiple of 25 and 13, it is 325. Usually, this is written as

lcm(25,13) = 325


The lcm of 25 and 13 can be obtained like this:
  • The multiples of 25 are … , 300, 325, 350, ….
  • The multiples of 13 are …, 312, 325, 338, …
  • The common multiples of 25 and 13 are n x 325, intersecting the two sets above, .
  • In the intersection multiples of 25 ∩ multiples of 13 the least positive element is 325.
  • Therefore, the least common multiple of 25 and 13 is 325.

Taking the above into account you also know how to find all the common multiples of 25 and 13, not just the smallest. In the next section we show you how to calculate the lcm of twenty-five and thirteen by means of two more methods.

How to find the LCM of 25 and 13

The least common multiple of 25 and 13 can be computed by using the greatest common factor aka gcf of 25 and 13. This is the easiest approach:

lcm (25,13) = = 325



Alternatively, the lcm of 25 and 13 can be found using the prime factorization of 25 and 13:
  • The prime factorization of 25 is: 5 x 5
  • The prime factorization of 13 is: 13
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(25,25) = 325

In any case, the easiest way to compute the result for two numbers like 25 and 13 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 25,132,2. 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 25 and 13

What is the least common multiple of 25 and 13 used for? Answer: It is helpful for adding and subtracting fractions like 1/25 and 1/13. Just multiply the dividends and divisors by 13 and 25, respectively, such that the divisors have the value of 325, the lcm of 25 and 13.

. .

Next, we shed a light on the mathematical properties.

Properties of LCM of 25 and 13

The most important properties of the lcm(25,13) are:

  • Commutative property: lcm(25,13) = lcm(13,25)
  • Associative property: lcm(25,13,n) = lcm(lcm(13,25),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 twenty-five / thirteen by using the the search form in the sidebar of this page.

Questions and comments are really appreciated. Use the form below or send us a mail to get in touch.

Please hit the sharing buttons if our article about the least common multiple of 25 and 13 has been useful to you, and make sure to bookmark our site.

If you have some time left check out the related sites and resources in the sidebar of this site.

Thanks for your visit.

– Article written by Mark, last updated on August 8th, 2023