Question

Two positive integers a and b can be written as a = x³y² and b = xy³, where x and y are prime numbers. Find HCF(a, b) and LCM(a, b).

Answer 1

It is given that, a = x³y² and b = xy³, where x and y are prime numbers.

$$\begin{gathered} \mathrm{LCM}\left(a,b\right)=\mathrm{LCM}\left(x^3{y}^2,x{y}^3\right) \\ =\mathrm{The}\mathrm{highest}\mathrm{of}\mathrm{indices}\mathrm{of}x\mathrm{and}y \\ =x^3{y}^3 \\ \mathrm{HCF}\left(a,b\right)=\mathrm{HCF}\left(x^3{y}^2,x{y}^3\right) \\ =\mathrm{The}\mathrm{lowest}\mathrm{of}\mathrm{indices}\mathrm{of}x\mathrm{and}y \\ =x{y}^2 \end{gathered}$$

Hence, HCF(a, b) = xy² and LCM(a, b) = x³y³.