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LCM of 80 and 84

The lcm of 80 and 84 is the smallest positive integer that divides the numbers 80 and 84 without a remainder. Spelled out, it is the least common multiple of 80 and 84. Here you can find the result for 80 and 84, along with a total of three methods for computing it.


1680

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 80 and 84, but also that of three or more integers including eighty and eighty-four for example. Keep reading to learn everything about the lcm (80,84) and the terms related to it.

What is the Least Common Multiple of 80 and 84?

If you just want to know what is the least common multiple of 80 and 84, it is 1680. Usually, this is written as

lcm(80,84) = 1680


The lcm of 80 and 84 can be obtained like this:
  • The multiples of 80 are … , 1600, 1680, 1760, ….
  • The multiples of 84 are …, 1596, 1680, 1764, …
  • The common multiples of 80 and 84 are n x 1680, intersecting the two sets above, .
  • In the intersection multiples of 80 ∩ multiples of 84 the least positive element is 1680.
  • Therefore, the least common multiple of 80 and 84 is 1680.

Taking the above into account you also know how to find all the common multiples of 80 and 84, not just the smallest. In the next section we show you how to calculate the lcm of eighty and eighty-four by means of two more methods.

How to find the LCM of 80 and 84

The least common multiple of 80 and 84 can be computed by using the greatest common factor aka gcf of 80 and 84. This is the easiest approach:

lcm (80,84) = = 1680



Alternatively, the lcm of 80 and 84 can be found using the prime factorization of 80 and 84:
  • The prime factorization of 80 is: 2 x 2 x 2 x 2 x 5
  • The prime factorization of 84 is: 2 x 2 x 3 x 7
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(80,80) = 1680

In any case, the easiest way to compute the result for two numbers like 80 and 84 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 80,842,2. 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 80 and 84

What is the least common multiple of 80 and 84 used for? Answer: It is helpful for adding and subtracting fractions like 1/80 and 1/84. Just multiply the dividends and divisors by 21 and 20, respectively, such that the divisors have the value of 1680, the lcm of 80 and 84.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 80 and 84

The most important properties of the lcm(80,84) are:

  • Commutative property: lcm(80,84) = lcm(84,80)
  • Associative property: lcm(80,84,n) = lcm(lcm(84,80),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 eighty / eighty-four 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