Question

What is the lcm of $60$ and $75$?

Answer 1

Determine the $\mathrm{lcm}\left(60,75\right)$.

LCM or the Least Common Multiple is the smallest number which can be divided by the given numbers.

The prime factorization of $60$ is $2\times 2\times 3\times 5$.

The prime factorization of $75$ is $3\times 5\times 5$.

Now, calculate the LCM of $60$ and $75$:

$\begin{array}{rcl}\mathrm{LCM}\left(60,75\right)& =& 2\times 2\times 3\times 5\times 5\\ & \Rightarrow & \mathrm{LCM}\left(60,75\right)=300\end{array}$

Hence, the required lcm of $60$ and $75$ is $300$.