LCM of 100 and 99


The lcm of 100 and 99 is the smallest positive integer that divides the numbers 100 and 99 without a remainder. Spelled out, it is the least common multiple of 100 and 99. Here you can find the lcm of 100 and 99, 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 99, but also that of three or more integers including hundred and ninety-nine for example. Keep reading to learn everything about the lcm (100,99) and the terms related to it.

What is the LCM of 100 and 99

If you just want to know what is the least common multiple of 100 and 99, it is 9900. Usually, this is written as

lcm(100,99) = 9900

The lcm of 100 and 99 can be obtained like this:

  • The multiples of 100 are ... , 9800, 9900, 10000, ....
  • The multiples of 99 are ..., 9801, 9900, 9999, ...
  • The common multiples of 100 and 99 are n x 9900, intersecting the two sets above, \hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}.
  • In the intersection multiples of 100 ∩ multiples of 99 the least positive element is 9900.
  • Therefore, the least common multiple of 100 and 99 is 9900.

Taking the above into account you also know how to find all the common multiples of 100 and 99, not just the smallest. In the next section we show you how to calculate the lcm of hundred and ninety-nine by means of two more methods.

How to find the LCM of 100 and 99

The least common multiple of 100 and 99 can be computed by using the greatest common factor aka gcf of 100 and 99. This is the easiest approach:

lcm (100,99) = \frac{100 \times 99}{gcf(100,99)} = \frac{9900}{1} = 9900

Alternatively, the lcm of 100 and 99 can be found using the prime factorization of 100 and 99:

  • The prime factorization of 100 is: 2 x 2 x 5 x 5
  • The prime factorization of 99 is: 3 x 3 x 11
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(100,100) = 9900

In any case, the easiest way to compute the lcm of two numbers like 100 and 99 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 100,99. Next hit the calculate button.

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Use of LCM of 100 and 99

What is the least common multiple of 100 and 99 used for? Answer: It is helpful for adding and subtracting fractions like 1/100 and 1/99. Just multiply the dividends and divisors by 99 and 100, respectively, such that the divisors have the value of 9900, the lcm of 100 and 99.

\frac{1}{100} + \frac{1}{99} = \frac{99}{9900} + \frac{100}{9900} = \frac{199}{9900}. \hspace{30px}\frac{1}{100} - \frac{1}{99} = \frac{99}{9900} - \frac{100}{9900} = \frac{-1}{9900}.

Properties of LCM of 100 and 99

The most important properties of the lcm(100,99) are:

  • Commutative property: lcm(100,99) = lcm(99,100)
  • Associative property: lcm(100,99,n) = lcm(lcm(99,100),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 99 is 9900. In common notation: lcm (100,99) = 9900.

If you have been searching for lcm 100 and 99 or lcm 100 99 then you have come to the correct page, too. The same is the true if you typed lcm for 100 and 99 in your favorite search engine.

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

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