This is a poorly-formed question, because there's no such thing as a uniform randomly-chosen integer. It's more accurate to say that the probability of gcd(m, n

This is a poorly-formed question, because there's no such thing as a uniform randomly-chosen integer. It's more accurate to say that the probability of gcd(m, n) = 1, with m and n chosen from {1, ..., N}, approaches 6/pi^2 as N -> infinity.