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LCM of 14 and 65

The lcm of 14 and 65 is the smallest positive integer that divides the numbers 14 and 65 without a remainder. Spelled out, it is the least common multiple of 14 and 65. Here you can find the result for 14 and 65, along with a total of three methods for computing it.


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This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 14 and 65, but also that of three or more integers including fourteen and sixty-five for example. Keep reading to learn everything about the lcm (14,65) and the terms related to it.

What is the Least Common Multiple of 14 and 65?

If you just want to know what is the least common multiple of 14 and 65, it is 910. Usually, this is written as

lcm(14,65) = 910


The lcm of 14 and 65 can be obtained like this:
  • The multiples of 14 are … , 896, 910, 924, ….
  • The multiples of 65 are …, 845, 910, 975, …
  • The common multiples of 14 and 65 are n x 910, intersecting the two sets above, .
  • In the intersection multiples of 14 ∩ multiples of 65 the least positive element is 910.
  • Therefore, the least common multiple of 14 and 65 is 910.

Taking the above into account you also know how to find all the common multiples of 14 and 65, not just the smallest. In the next section we show you how to calculate the lcm of fourteen and sixty-five by means of two more methods.

How to find the LCM of 14 and 65

The least common multiple of 14 and 65 can be computed by using the greatest common factor aka gcf of 14 and 65. This is the easiest approach:

lcm (14,65) = = 910



Alternatively, the lcm of 14 and 65 can be found using the prime factorization of 14 and 65:
  • The prime factorization of 14 is: 2 x 7
  • 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(14,14) = 910

In any case, the easiest way to compute the result for two numbers like 14 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 14,652,2. 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 14 and 65

What is the least common multiple of 14 and 65 used for? Answer: It is helpful for adding and subtracting fractions like 1/14 and 1/65. Just multiply the dividends and divisors by 65 and 14, respectively, such that the divisors have the value of 910, the lcm of 14 and 65.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 14 and 65

The most important properties of the lcm(14,65) are:

  • Commutative property: lcm(14,65) = lcm(65,14)
  • Associative property: lcm(14,65,n) = lcm(lcm(65,14),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 fourteen / 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