Cesagravero estimate- let a and b be integers chosen

Question

Cesàro estimate:-

Let a and b be integers chosen randomly. Show that the probability that gcd(a, b) = 1 is 6/π² using the following steps:

(a) Assume that the probability of gcd(a, b) = 1 is p. For any integer d it will happen that gcd(a, b) = d only if a and b are each multiples of d and gcd(a/d, b/d) = 1. Hence find the probability that gcd(a, b) = d in terms of p.

(b) Use the fact that sum of all those probabilities must be 1.