2007 AMC 12B Problem 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 $a+b+c+d$ ?

$\mathrm {(A)} 13\qquad \mathrm {(B)} 14\qquad \mathrm {(C)} 15\qquad \mathrm {(D)} 16\qquad \mathrm {(E)} 17$

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.