If the sum of two numbers is 55 and the H.C.F. and L.C.M of these numbers are…

To find the sum of the reciprocals of two numbers when their sum, H.C.F., and L.C.M. are known, you can use a simple algebraic relationship.

The Formula

• Let the two numbers be x and y. We want to find the sum of their reciprocals:

• Sum of reciprocals = 1/x + 1/y = (x + y) / (x * y)

Where:

(x + y) is the sum of the numbers.

(x * y) is the product of the numbers, which is also equal to H.C.F. * L.C.M.

Step-by-Step Calculation
Identify the given values:

• Sum of numbers (x + y) = 55

• H.C.F. = 5

• L.C.M. = 120

Calculate the product of the numbers:

• Product (x * y) = H.C.F. * L.C.M. = 5 * 120 = 600

Calculate the sum of reciprocals:

• Sum of reciprocals = (Sum of numbers) / (Product of numbers)

• Sum of reciprocals = 55 / 600

• Simplify the fraction by dividing both numerator and denominator by 5:

• Sum of reciprocals = 11 / 120