The HCF and LCM of two numbers are 4 and 288 respectively. Find the numbers and how many such pairs are possible.

 

Dear Student,

We know that, Product of two numbers = $\mathrm{H}.\mathrm{C}.\mathrm{F}\times \mathrm{L}.\mathrm{C}.\mathrm{M}$
Suppose other two numbers are A and B.so we can write;
$$\begin{gathered} \mathrm{A}\times \mathrm{B} = 4\times 288 \\ \Rightarrow \mathrm{A} = \frac{4\times 288}{\mathrm{B}} \end{gathered}$$
Taking  B = 32; then $\mathrm{A} = \frac{4\times 288}{32} = 36$
Therefore other number is 36 if one number is 32.

So, (32 36) is one of the pair that satisfies the above conditions.

Regards.