LCM of 100 and 80


The lcm of 100 and 80 is the smallest positive integer that divides the numbers 100 and 80 without a remainder. Spelled out, it is the least common multiple of 100 and 80. Here you can find the lcm of 100 and 80, 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 100 and 80, but also that of three or more integers including hundred and eighty for example. Keep reading to learn everything about the lcm (100,80) and the terms related to it.

What is the LCM of 100 and 80

If you just want to know what is the least common multiple of 100 and 80, it is 400. Usually, this is written as

lcm(100,80) = 400

The lcm of 100 and 80 can be obtained like this:

  • The multiples of 100 are ... , 300, 400, 500, ....
  • The multiples of 80 are ..., 320, 400, 480, ...
  • The common multiples of 100 and 80 are n x 400, intersecting the two sets above, \hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}.
  • In the intersection multiples of 100 ∩ multiples of 80 the least positive element is 400.
  • Therefore, the least common multiple of 100 and 80 is 400.

Taking the above into account you also know how to find all the common multiples of 100 and 80, not just the smallest. In the next section we show you how to calculate the lcm of hundred and eighty by means of two more methods.

How to find the LCM of 100 and 80

The least common multiple of 100 and 80 can be computed by using the greatest common factor aka gcf of 100 and 80. This is the easiest approach:

lcm (100,80) = \frac{100 \times 80}{gcf(100,80)} = \frac{8000}{20} = 400

Alternatively, the lcm of 100 and 80 can be found using the prime factorization of 100 and 80:

  • The prime factorization of 100 is: 2 x 2 x 5 x 5
  • The prime factorization of 80 is: 2 x 2 x 2 x 2 x 5
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(100,100) = 400

In any case, the easiest way to compute the lcm of two numbers like 100 and 80 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 100,80. Next hit the calculate button.

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Use of LCM of 100 and 80

What is the least common multiple of 100 and 80 used for? Answer: It is helpful for adding and subtracting fractions like 1/100 and 1/80. Just multiply the dividends and divisors by 4 and 5, respectively, such that the divisors have the value of 400, the lcm of 100 and 80.

\frac{1}{100} + \frac{1}{80} = \frac{4}{400} + \frac{5}{400} = \frac{9}{400}. \hspace{30px}\frac{1}{100} - \frac{1}{80} = \frac{4}{400} - \frac{5}{400} = \frac{-1}{400}.

Properties of LCM of 100 and 80

The most important properties of the lcm(100,80) are:

  • Commutative property: lcm(100,80) = lcm(80,100)
  • Associative property: lcm(100,80,n) = lcm(lcm(80,100),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 100 and 80 is 400. In common notation: lcm (100,80) = 400.

If you have been searching for lcm 100 and 80 or lcm 100 80 then you have come to the correct page, too. The same is the true if you typed lcm for 100 and 80 in your favorite search engine.

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

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