Question

If the HCF and LCM of two positive integers a and b are x and y respectively, then `(x^2y^2)/(a^2b^2)` = ______.

Answer 1

If the HCF and LCM of two positive integers a and b are x and y respectively, then `(x^2y^2)/(a^2b^2)` = 1.

Explanation:

HCF × LCM = a × b, so xy = ab.

Therefore `(x^2y^2)/(a^2 b^2) = ((xy)/(ab))^2`

= 1²

= 1