LCM of 60 and 96


The lcm of 60 and 96 is the smallest positive integer that divides the numbers 60 and 96 without a remainder. Spelled out, it is the least common multiple of 60 and 96. Here you can find the lcm of 60 and 96, 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 60 and 96, but also that of three or more integers including sixty and ninety-six for example. Keep reading to learn everything about the lcm (60,96) and the terms related to it.

What is the LCM of 60 and 96

If you just want to know what is the least common multiple of 60 and 96, it is 480. Usually, this is written as

lcm(60,96) = 480

The lcm of 60 and 96 can be obtained like this:

  • The multiples of 60 are …, 420, 480, 540, ….
  • The multiples of 96 are …, 384, 480, 576, …
  • The common multiples of 60 and 96 are n x 480, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 60 ∩ multiples of 96 the least positive element is 480.
  • Therefore, the least common multiple of 60 and 96 is 480.

Taking the above into account you also know how to find all the common multiples of 60 and 96, not just the smallest. In the next section we show you how to calculate the lcm of sixty and ninety-six by means of two more methods.

How to find the LCM of 60 and 96

The least common multiple of 60 and 96 can be computed by using the greatest common factor aka gcf of 60 and 96. This is the easiest approach:

lcm (60,96) = $\frac{60 \times 96}{gcf(60,96)} = \frac{5760}{12}$ = 480

Alternatively, the lcm of 60 and 96 can be found using the prime factorization of 60 and 96:

  • The prime factorization of 60 is: 2 x 2 x 3 x 5
  • The prime factorization of 96 is: 2 x 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(60,60) = 480

In any case, the easiest way to compute the lcm of two numbers like 60 and 96 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 60,96. Push the button only to start over.

The lcm is...
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Use of LCM of 60 and 96

What is the least common multiple of 60 and 96 used for? Answer: It is helpful for adding and subtracting fractions like 1/60 and 1/96. Just multiply the dividends and divisors by 8 and 5, respectively, such that the divisors have the value of 480, the lcm of 60 and 96.

$\frac{1}{60} + \frac{1}{96} = \frac{8}{480} + \frac{5}{480} = \frac{13}{480}$. $\hspace{30px}\frac{1}{60} – \frac{1}{96} = \frac{8}{480} – \frac{5}{480} = \frac{3}{480}$.

Properties of LCM of 60 and 96

The most important properties of the lcm(60,96) are:

  • Commutative property: lcm(60,96) = lcm(96,60)
  • Associative property: lcm(60,96,n) = lcm(lcm(96,60),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 60 and 96 is 480. In common notation: lcm (60,96) = 480.

If you have been searching for lcm 60 and 96 or lcm 60 96 then you have come to the correct page, too. The same is the true if you typed lcm for 60 and 96 in your favorite search engine.

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

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