LCM of 48 and 72


The lcm of 48 and 72 is the smallest positive integer that divides the numbers 48 and 72 without a remainder. Spelled out, it is the least common multiple of 48 and 72. Here you can find the lcm of 48 and 72, 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 48 and 72, but also that of three or more integers including forty-eight and seventy-two for example. Keep reading to learn everything about the lcm (48,72) and the terms related to it.

What is the LCM of 48 and 72

If you just want to know what is the least common multiple of 48 and 72, it is 144. Usually, this is written as

lcm(48,72) = 144

The lcm of 48 and 72 can be obtained like this:

  • The multiples of 48 are …, 96, 144, 192, ….
  • The multiples of 72 are …, 72, 144, 216, …
  • The common multiples of 48 and 72 are n x 144, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 48 ∩ multiples of 72 the least positive element is 144.
  • Therefore, the least common multiple of 48 and 72 is 144.

Taking the above into account you also know how to find all the common multiples of 48 and 72, not just the smallest. In the next section we show you how to calculate the lcm of forty-eight and seventy-two by means of two more methods.

How to find the LCM of 48 and 72

The least common multiple of 48 and 72 can be computed by using the greatest common factor aka gcf of 48 and 72. This is the easiest approach:

lcm (48,72) = $\frac{48 \times 72}{gcf(48,72)} = \frac{3456}{24}$ = 144

Alternatively, the lcm of 48 and 72 can be found using the prime factorization of 48 and 72:

  • The prime factorization of 48 is: 2 x 2 x 2 x 2 x 3
  • The prime factorization of 72 is: 2 x 2 x 2 x 3 x 3
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(48,48) = 144

In any case, the easiest way to compute the lcm of two numbers like 48 and 72 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 48,72. Push the button only to start over.

The lcm is...
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Use of LCM of 48 and 72

What is the least common multiple of 48 and 72 used for? Answer: It is helpful for adding and subtracting fractions like 1/48 and 1/72. Just multiply the dividends and divisors by 3 and 2, respectively, such that the divisors have the value of 144, the lcm of 48 and 72.

$\frac{1}{48} + \frac{1}{72} = \frac{3}{144} + \frac{2}{144} = \frac{5}{144}$. $\hspace{30px}\frac{1}{48} – \frac{1}{72} = \frac{3}{144} – \frac{2}{144} = \frac{1}{144}$.

Properties of LCM of 48 and 72

The most important properties of the lcm(48,72) are:

  • Commutative property: lcm(48,72) = lcm(72,48)
  • Associative property: lcm(48,72,n) = lcm(lcm(72,48),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 48 and 72 is 144. In common notation: lcm (48,72) = 144.

If you have been searching for lcm 48 and 72 or lcm 48 72 then you have come to the correct page, too. The same is the true if you typed lcm for 48 and 72 in your favorite search engine.

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

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