LCM of 98 and 48


The lcm of 98 and 48 is the smallest positive integer that divides the numbers 98 and 48 without a remainder. Spelled out, it is the least common multiple of 98 and 48. Here you can find the lcm of 98 and 48, 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 98 and 48, but also that of three or more integers including ninety-eight and forty-eight for example. Keep reading to learn everything about the lcm (98,48) and the terms related to it.

What is the LCM of 98 and 48

If you just want to know what is the least common multiple of 98 and 48, it is 2352. Usually, this is written as

lcm(98,48) = 2352

The lcm of 98 and 48 can be obtained like this:

  • The multiples of 98 are …, 2254, 2352, 2450, ….
  • The multiples of 48 are …, 2304, 2352, 2400, …
  • The common multiples of 98 and 48 are n x 2352, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 98 ∩ multiples of 48 the least positive element is 2352.
  • Therefore, the least common multiple of 98 and 48 is 2352.

Taking the above into account you also know how to find all the common multiples of 98 and 48, not just the smallest. In the next section we show you how to calculate the lcm of ninety-eight and forty-eight by means of two more methods.

How to find the LCM of 98 and 48

The least common multiple of 98 and 48 can be computed by using the greatest common factor aka gcf of 98 and 48. This is the easiest approach:

lcm (98,48) = $\frac{98 \times 48}{gcf(98,48)} = \frac{4704}{2}$ = 2352

Alternatively, the lcm of 98 and 48 can be found using the prime factorization of 98 and 48:

  • The prime factorization of 98 is: 2 x 7 x 7
  • The prime factorization of 48 is: 2 x 2 x 2 x 2 x 3
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(98,98) = 2352

In any case, the easiest way to compute the lcm of two numbers like 98 and 48 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 98,48. Push the button only to start over.

The lcm is...
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Use of LCM of 98 and 48

What is the least common multiple of 98 and 48 used for? Answer: It is helpful for adding and subtracting fractions like 1/98 and 1/48. Just multiply the dividends and divisors by 24 and 49, respectively, such that the divisors have the value of 2352, the lcm of 98 and 48.

$\frac{1}{98} + \frac{1}{48} = \frac{24}{2352} + \frac{49}{2352} = \frac{73}{2352}$. $\hspace{30px}\frac{1}{98} – \frac{1}{48} = \frac{24}{2352} – \frac{49}{2352} = \frac{-25}{2352}$.

Properties of LCM of 98 and 48

The most important properties of the lcm(98,48) are:

  • Commutative property: lcm(98,48) = lcm(48,98)
  • Associative property: lcm(98,48,n) = lcm(lcm(48,98),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 98 and 48 is 2352. In common notation: lcm (98,48) = 2352.

If you have been searching for lcm 98 and 48 or lcm 98 48 then you have come to the correct page, too. The same is the true if you typed lcm for 98 and 48 in your favorite search engine.

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

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