The difference between two numbers is 15 and their HCF and LCM are 3 and 108 respectively. Find the difference between their reciprocals.

$\frac{5}{108}$

Let the two numbers are x and y

⇒ x – y = 15 and xy = 3 × 108 [Product of two number = HCF × LCM]

⇒ \(\frac{1}{y}\) – \(\frac{1}{x}\)

⇒ \(\frac{x - y}{xy}\)

⇒ \(\frac{15}{3 × 108}\)

⇒ \(\frac{5}{108}\)