LCM of 100 and 98


The lcm of 100 and 98 is the smallest positive integer that divides the numbers 100 and 98 without a remainder. Spelled out, it is the least common multiple of 100 and 98. Here you can find the lcm of 100 and 98, 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 98, but also that of three or more integers including hundred and ninety-eight for example. Keep reading to learn everything about the lcm (100,98) and the terms related to it.

What is the LCM of 100 and 98

If you just want to know what is the least common multiple of 100 and 98, it is 4900. Usually, this is written as

lcm(100,98) = 4900

The lcm of 100 and 98 can be obtained like this:

  • The multiples of 100 are …, 4800, 4900, 5000, ….
  • The multiples of 98 are …, 4802, 4900, 4998, …
  • The common multiples of 100 and 98 are n x 4900, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 100 ∩ multiples of 98 the least positive element is 4900.
  • Therefore, the least common multiple of 100 and 98 is 4900.

Taking the above into account you also know how to find all the common multiples of 100 and 98, not just the smallest. In the next section we show you how to calculate the lcm of hundred and ninety-eight by means of two more methods.

How to find the LCM of 100 and 98

The least common multiple of 100 and 98 can be computed by using the greatest common factor aka gcf of 100 and 98. This is the easiest approach:

lcm (100,98) = $\frac{100 \times 98}{gcf(100,98)} = \frac{9800}{2}$ = 4900

Alternatively, the lcm of 100 and 98 can be found using the prime factorization of 100 and 98:

  • The prime factorization of 100 is: 2 x 2 x 5 x 5
  • The prime factorization of 98 is: 2 x 7 x 7
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(100,100) = 4900

In any case, the easiest way to compute the lcm of two numbers like 100 and 98 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 100,98. Push the button only to start over.

The lcm is...
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Use of LCM of 100 and 98

What is the least common multiple of 100 and 98 used for? Answer: It is helpful for adding and subtracting fractions like 1/100 and 1/98. Just multiply the dividends and divisors by 49 and 50, respectively, such that the divisors have the value of 4900, the lcm of 100 and 98.

$\frac{1}{100} + \frac{1}{98} = \frac{49}{4900} + \frac{50}{4900} = \frac{99}{4900}$. $\hspace{30px}\frac{1}{100} – \frac{1}{98} = \frac{49}{4900} – \frac{50}{4900} = \frac{-1}{4900}$.

Properties of LCM of 100 and 98

The most important properties of the lcm(100,98) are:

  • Commutative property: lcm(100,98) = lcm(98,100)
  • Associative property: lcm(100,98,n) = lcm(lcm(98,100),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 98 is 4900. In common notation: lcm (100,98) = 4900.

If you have been searching for lcm 100 and 98 or lcm 100 98 then you have come to the correct page, too. The same is the true if you typed lcm for 100 and 98 in your favorite search engine.

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

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