how to compute $\gcd(\frac{a}{b},\frac{c}{d})$?

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is there a formula for

$gcd(\frac{a}{b},\frac{c}{d})?$

I'm conjeturing $gcd(\frac{a}{b},\frac{c}{d})=\frac{gcd(a,c))}{lcm(b,d)}$ but how to prove it?