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LCM of 100 and 65

The lcm of 100 and 65 is the smallest positive integer that divides the numbers 100 and 65 without a remainder. Spelled out, it is the least common multiple of 100 and 65. Here you can find the result for 100 and 65, along with a total of three methods for computing it.


1300

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 100 and 65, but also that of three or more integers including hundred and sixty-five for example. Keep reading to learn everything about the lcm (100,65) and the terms related to it.

What is the Least Common Multiple of 100 and 65?

If you just want to know what is the least common multiple of 100 and 65, it is 1300. Usually, this is written as

lcm(100,65) = 1300


The lcm of 100 and 65 can be obtained like this:
  • The multiples of 100 are … , 1200, 1300, 1400, ….
  • The multiples of 65 are …, 1235, 1300, 1365, …
  • The common multiples of 100 and 65 are n x 1300, intersecting the two sets above, .
  • In the intersection multiples of 100 ∩ multiples of 65 the least positive element is 1300.
  • Therefore, the least common multiple of 100 and 65 is 1300.

Taking the above into account you also know how to find all the common multiples of 100 and 65, not just the smallest. In the next section we show you how to calculate the lcm of hundred and sixty-five by means of two more methods.

How to find the LCM of 100 and 65

The least common multiple of 100 and 65 can be computed by using the greatest common factor aka gcf of 100 and 65. This is the easiest approach:

lcm (100,65) = = 1300



Alternatively, the lcm of 100 and 65 can be found using the prime factorization of 100 and 65:
  • The prime factorization of 100 is: 2 x 2 x 5 x 5
  • The prime factorization of 65 is: 5 x 13
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(100,100) = 1300

In any case, the easiest way to compute the result for two numbers like 100 and 65 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 100,652,2. 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 100 and 65

What is the least common multiple of 100 and 65 used for? Answer: It is helpful for adding and subtracting fractions like 1/100 and 1/65. Just multiply the dividends and divisors by 13 and 20, respectively, such that the divisors have the value of 1300, the lcm of 100 and 65.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 100 and 65

The most important properties of the lcm(100,65) are:

  • Commutative property: lcm(100,65) = lcm(65,100)
  • Associative property: lcm(100,65,n) = lcm(lcm(65,100),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 hundred / sixty-five 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