Question

What is the LCM of $9$ and $12$?

Answer 1

Determine the LCM of $9$ and $12$.

Apply the prime factorization method to find the lcm of the given numbers:

The prime factorization of $9$ is $3\times 3$.

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

Calculate the LCM of $9$ and $12$:

$\begin{array}{rcl}\mathrm{LCM}\left(9,12\right)& =& 2\times 2\times 3\times 3\end{array}$

$\begin{array}{rcl}\therefore \mathrm{LCM}\left(9,12\right)& =& 36\end{array}$

Hence, the required LCM is $\mathrm{LCM}(9,12)=36$.