Question

The H.C.F. of two numbers is $9$ and their L.C.M. is $108$. If the first number is $36$, find the second.

Answer 1

Finding the second number

$$\begin{gathered} \text{Product of the number =LCM×HCF} \\ \text{⇒First number×Second number=LCM×HCF} \\ \text{⇒36×Second number =108×9} \\ \text{⇒Second number =}\frac{108\times 9}{36} \\ \Rightarrow \text{Second number}=27 \end{gathered}$$

Hence, the other number is $27$.