Question

Find the least common multiple of the following polynomials $9\left(x+2\right)\left(2x-1\right)$ and $3\left(x+2\right)$.

Answer 1

Find the least common multiple of $9\left(x+2\right)\left(2x-1\right)$ and $3\left(x+2\right)$:

The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.

Thus, the least common multiple is as follows:

$\begin{array}{rcl}9\left(x+2\right)\left(2x-1\right)& =& 3·3·\left(x+2\right)·\left(2x-1\right)\\ 3\left(x+2\right)& =& 3·\left(x+2\right)\\ & \Rightarrow & \mathrm{LCM}=3·\left(x+2\right)·3·\left(2x-1\right)\\ & \Rightarrow & \mathrm{LCM}=9\left(x+2\right)\left(2x-1\right)\end{array}$

Hence, the least common multiple of $9\left(x+2\right)\left(2x-1\right)$ and $3\left(x+2\right)$ is $9\left(x+2\right)\left(2x-1\right)$.