Question

The HCF and LCM of two numbers are $33$ and $264$ respectively. When the first number is completely divided by $2$ the quotient is $33$ the other number is

Answer 1

Given:

• H.C.F $=33$
• L.C.M $=264$

When the first number is completely divided by $2$, then the quotient is $33$ and the remainder is $0$.

Let the number be $\mathrm{x}$

$$\begin{gathered} \frac{\mathrm{x}}{2}=33 \\ \Rightarrow \mathrm{x}=2\left(33\right) \\ \Rightarrow \mathrm{x}=66 \end{gathered}$$

Let the other number be$\mathrm{y}$.

$$\begin{gathered} \mathrm{H}.\mathrm{C}.\mathrm{F}\times \mathrm{L}.\mathrm{C}.\mathrm{M}=\mathrm{Product}\mathrm{of}\mathrm{two}\mathrm{numbers} \\ \Rightarrow 33\times 264=\mathrm{x}\times \mathrm{y} \\ \Rightarrow \mathrm{y}=\frac{33\times 264}{66} \\ \Rightarrow \mathrm{y}=132 \end{gathered}$$

Hence, the other number is $132$..