The **lcm of 24 and 8** is the smallest positive integer that divides the numbers 24 and 8 without a remainder. Spelled out, it is the least common multiple of 24 and 8. Here you can find the lcm of 24 and 8, 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 24 and 8, but also that of three or more integers including twenty-four and eight for example. Keep reading to learn everything about the lcm (24,8) and the terms related to it.

## What is the LCM of 24 and 8

If you just want to know *what is the least common multiple of 24 and 8*, it is **24**. Usually, this is written as

**lcm(24,8) = 24**

The lcm of 24 and 8 can be obtained like this:

- The multiples of 24 are …, 0, 24, 48, ….
- The multiples of 8 are …, 16, 24, 32, …
- The
*common*multiples of 24 and 8 are n x 24, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$. - In the intersection multiples of 24 ∩ multiples of 8 the
*least*positive element is 24. - Therefore, the
**least common multiple of 24 and 8 is 24**.

Taking the above into account you also know how to find *all* the common multiples of 24 and 8, not just the smallest. In the next section we show you how to calculate the lcm of twenty-four and eight by means of two more methods.

## How to find the LCM of 24 and 8

The least common multiple of 24 and 8 can be computed by using the greatest common factor aka gcf of 24 and 8. This is the easiest approach:

Alternatively, the lcm of 24 and 8 can be found using the prime factorization of 24 and 8:

- The prime factorization of 24 is: 2 x 2 x 2 x 3
- The prime factorization of 8 is: 2 x 2 x 2
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(24,24) = 24

In any case, the easiest way to compute the lcm of two numbers like 24 and 8 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 24,8. Push the button only to start over.

## Use of LCM of 24 and 8

What is the least common multiple of 24 and 8 used for? Answer: It is helpful for adding and subtracting fractions like 1/24 and 1/8. Just multiply the dividends and divisors by 1 and 3, respectively, such that the divisors have the value of 24, the lcm of 24 and 8.

$\frac{1}{24} + \frac{1}{8} = \frac{1}{24} + \frac{3}{24} = \frac{4}{24}$. $\hspace{30px}\frac{1}{24} – \frac{1}{8} = \frac{1}{24} – \frac{3}{24} = \frac{-2}{24}$.

## Properties of LCM of 24 and 8

The most important properties of the lcm(24,8) are:

- Commutative property: lcm(24,8) = lcm(8,24)
- Associative property: lcm(24,8,n) = lcm(lcm(8,24),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 24 and 8 is 24. In common notation: lcm (24,8) = 24.

If you have been searching for lcm 24 and 8 or lcm 24 8 then you have come to the correct page, too. The same is the true if you typed lcm for 24 and 8 in your favorite search engine.

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

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