Show that two numbers divided by their GCD are coprime
If $d'>1$ divides both $\frac{a}{d}$ and $\frac{b}{d}$ then $dd'> d$ divides $a$ and $b$, contradicting the fact that $d$ is the greatest common divisor of $a$ and $b$.
If $d'>1$ divides both $\frac{a}{d}$ and $\frac{b}{d}$ then $dd'> d$ divides $a$ and $b$, contradicting the fact that $d$ is the greatest common divisor of $a$ and $b$.