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

\(\frac{5 }{108}\)

⇒ (Product of two other factors) × HCF = LCM

⇒ (a × b) × 3 = 108

⇒ (a × b) = 36

So a and b = 9 and 4

Therefore, numbers are:

= (a × HCF), (b × HCF)

= (9 × 3), (4 × 3) = 27 , 12

ATQ,

Difference = 27 - 12 = 15 (given)

So, Difference of their reciprocal is

⇒ \(\frac{1}{12}\) - \(\frac{1}{27}\) = \(\frac{9\;-\;4}{108}\) = \(\frac{5}{108}\)