Since \(d = (a, b)\), then \(d\) is also the smallest positive linear combination of \(a\) and \(b\) (click here to see why):
$$d = ha + kb$$
Let \(a = dx\) and \(b=dy\) where x, y ∈ ℤ:
$$\begin{gathered} d = hdx + kdy\\ 1 = hx + ky \end{gathered}$$
This shows that \((x, y) = 1\) (since \(hx + ky = 1 is the smallest positive linear combination\)), or in other words, \((a/d, b/d) = 1\).