The sum of two numbers is 18 and their HCF and LCM are 3 and 54 respectively. What will be the sum of their reciprocals?

$\frac{1}{9}$

H.C.F. = 3

L.C.M. = 34

Sum of two numbers = 18

 Let the two numbers be x and y.

⇒ x + y = 18

Also, xy = 3 × 54  = 162

Sum of reciprocal of these numbers,

\(\frac{1}{x} + \frac{1}{y}\) = \(\frac{x + y}{xy}\)

\(\frac{x + y}{xy}\)  = \(\frac{18}{162}\) = \(\frac{1}{9}\)