LCM of 100 and 91


The lcm of 100 and 91 is the smallest positive integer that divides the numbers 100 and 91 without a remainder. Spelled out, it is the least common multiple of 100 and 91. Here you can find the lcm of 100 and 91, 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 91, but also that of three or more integers including hundred and ninety-one for example. Keep reading to learn everything about the lcm (100,91) and the terms related to it.

What is the LCM of 100 and 91

If you just want to know what is the least common multiple of 100 and 91, it is 9100. Usually, this is written as

lcm(100,91) = 9100

The lcm of 100 and 91 can be obtained like this:

  • The multiples of 100 are …, 9000, 9100, 9200, ….
  • The multiples of 91 are …, 9009, 9100, 9191, …
  • The common multiples of 100 and 91 are n x 9100, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 100 ∩ multiples of 91 the least positive element is 9100.
  • Therefore, the least common multiple of 100 and 91 is 9100.

Taking the above into account you also know how to find all the common multiples of 100 and 91, not just the smallest. In the next section we show you how to calculate the lcm of hundred and ninety-one by means of two more methods.

How to find the LCM of 100 and 91

The least common multiple of 100 and 91 can be computed by using the greatest common factor aka gcf of 100 and 91. This is the easiest approach:

lcm (100,91) = $\frac{100 \times 91}{gcf(100,91)} = \frac{9100}{1}$ = 9100

Alternatively, the lcm of 100 and 91 can be found using the prime factorization of 100 and 91:

  • The prime factorization of 100 is: 2 x 2 x 5 x 5
  • The prime factorization of 91 is: 7 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) = 9100

In any case, the easiest way to compute the lcm of two numbers like 100 and 91 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 100,91. Push the button only to start over.

The lcm is...
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Use of LCM of 100 and 91

What is the least common multiple of 100 and 91 used for? Answer: It is helpful for adding and subtracting fractions like 1/100 and 1/91. Just multiply the dividends and divisors by 91 and 100, respectively, such that the divisors have the value of 9100, the lcm of 100 and 91.

$\frac{1}{100} + \frac{1}{91} = \frac{91}{9100} + \frac{100}{9100} = \frac{191}{9100}$. $\hspace{30px}\frac{1}{100} – \frac{1}{91} = \frac{91}{9100} – \frac{100}{9100} = \frac{-9}{9100}$.

Properties of LCM of 100 and 91

The most important properties of the lcm(100,91) are:

  • Commutative property: lcm(100,91) = lcm(91,100)
  • Associative property: lcm(100,91,n) = lcm(lcm(91,100),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 91 is 9100. In common notation: lcm (100,91) = 9100.

If you have been searching for lcm 100 and 91 or lcm 100 91 then you have come to the correct page, too. The same is the true if you typed lcm for 100 and 91 in your favorite search engine.

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

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