The sum of two numbers is 55. Their HCF is 5 and their LCM is 120. What is the sum of the reciprocals of the two numbers?

Concept / Approach

• For positive integers a and b, ab = HCF × LCM.
• The sum of reciprocals is (a + b)/ab.

Step-by-step calculation
a + b = 55ab = 5 × 120 = 600Sum of reciprocals = (a + b)/ab = 55/600 = 11/120

Final Answer
11/120