Question

What is the lcm of $8$, $10$, and $12$?

Answer 1

Determine the LCM of $8$, $10$, and $12$ by using the prime factorization method.

The prime factorization of $8$ is $2\times 2\times 2$.

The prime factorization of $10$ is $2\times 5$.

The prime factorization of $12$ is $2\times 2\times 3$.

Now, calculate the lcm of the given numbers:

$\begin{array}{rcl}\mathrm{LCM}\left(8,10,12\right)& =& 2\times 2\times 2\times 5\times 3\end{array}$

$\begin{array}{rcl}\therefore \mathrm{LCM}\left(8,10,12\right)& =& 120\end{array}$

Hence, the required LCM is $\begin{array}{rcl}\mathrm{LCM}\left(8,10,12\right)& =& 120\end{array}$.