LCM of 84 and 100


The lcm of 84 and 100 is the smallest positive integer that divides the numbers 84 and 100 without a remainder. Spelled out, it is the least common multiple of 84 and 100. Here you can find the lcm of 84 and 100, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the lcm of 84 and 100, but also that of three or more integers including eighty-four and hundred for example. Keep reading to learn everything about the lcm (84,100) and the terms related to it.

What is the LCM of 84 and 100

If you just want to know what is the least common multiple of 84 and 100, it is 2100. Usually, this is written as

lcm(84,100) = 2100

The lcm of 84 and 100 can be obtained like this:

  • The multiples of 84 are …, 2016, 2100, 2184, ….
  • The multiples of 100 are …, 2000, 2100, 2200, …
  • The common multiples of 84 and 100 are n x 2100, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 84 ∩ multiples of 100 the least positive element is 2100.
  • Therefore, the least common multiple of 84 and 100 is 2100.

Taking the above into account you also know how to find all the common multiples of 84 and 100, not just the smallest. In the next section we show you how to calculate the lcm of eighty-four and hundred by means of two more methods.

How to find the LCM of 84 and 100

The least common multiple of 84 and 100 can be computed by using the greatest common factor aka gcf of 84 and 100. This is the easiest approach:

lcm (84,100) = $\frac{84 \times 100}{gcf(84,100)} = \frac{8400}{4}$ = 2100

Alternatively, the lcm of 84 and 100 can be found using the prime factorization of 84 and 100:

  • The prime factorization of 84 is: 2 x 2 x 3 x 7
  • The prime factorization of 100 is: 2 x 2 x 5 x 5
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(84,84) = 2100

In any case, the easiest way to compute the lcm of two numbers like 84 and 100 is by using our calculator below. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 84,100. Push the button only to start over.

The lcm is...
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Use of LCM of 84 and 100

What is the least common multiple of 84 and 100 used for? Answer: It is helpful for adding and subtracting fractions like 1/84 and 1/100. Just multiply the dividends and divisors by 25 and 21, respectively, such that the divisors have the value of 2100, the lcm of 84 and 100.

$\frac{1}{84} + \frac{1}{100} = \frac{25}{2100} + \frac{21}{2100} = \frac{46}{2100}$. $\hspace{30px}\frac{1}{84} – \frac{1}{100} = \frac{25}{2100} – \frac{21}{2100} = \frac{4}{2100}$.

Properties of LCM of 84 and 100

The most important properties of the lcm(84,100) are:

  • Commutative property: lcm(84,100) = lcm(100,84)
  • Associative property: lcm(84,100,n) = lcm(lcm(100,84),n) $\hspace{10px}n\neq 0 \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$

The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.

To sum up, the lcm of 84 and 100 is 2100. In common notation: lcm (84,100) = 2100.

If you have been searching for lcm 84 and 100 or lcm 84 100 then you have come to the correct page, too. The same is the true if you typed lcm for 84 and 100 in your favorite search engine.

Note that you can find the least common multiple of many integer pairs including eighty-four / hundred by using the search form in the sidebar of this page.

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