If two positive integers $a$ and $b$ are written as $a=x^{3} y^{2}$ and $b=x y^{3}$, where $x, y$ ar

Question

If two positive integers $a$ and $b$ are written as $a=x^{3} y^{2}$ and $b=x y^{3}$, where $x, y$ are prime numbers, then the result obtained by dividing the product of the positive integers by the $\operatorname{LCM}(a, b)$ is\

Professor PC Thomas Classes · Answer

(b) : Given $a=x^{3} y^{2}=x 	imes x 	imes x 	imes y 	imes y$\ $b=x y^{3}=x 	imes y 	imes y 	imes y$ \ LCM(a, b)= x $	imes$ x $	imes$ x $	imes$ y $	imes$ y $	imes$ y=x$^{3}$ y$^{3}$ \Now, $\frac{a 	imes b}{\operatorname{LCM}(a, b)}=\frac{x^{3} y^{2} 	imes x y^{3}}{x^{3} y^{3}}=x y^{2}$\