Question 36

The sum of two numbers is 65 and the HCF of the two numbers is 5. If the LCM of the two numbers is 180, what is the sum of the reciprocals of the two numbers?

Solution

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Let the numbers be ha and hb. HCF of the numbers = h and LCM of the numbers = hab.
Sum of reciprocals = (a+b)/hab
h(a+b) = 65
h = 5
(a+b) = 13
hab = LCM = 180
So, sum of reciprocals = 13/180

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