Question 20
The parallelogram bounded by the lines $y=ax+c,$ $y=ax+d,$ $y=bx+c,$ and $y=bx+d$ has area $18.$ The parallelogram bounded by the lines $y=ax+c,$ $y=ax-d,$ $y=bx+c,$ and $y=bx-d$ has area $72.$ Given that $a,$ $b,$ $c,$ and $d$ are positive integers, what is the smallest possible value of $a+b+c+d?$