KöMaL 2024 C1822

The diagonals $AC$ and $BD$ of convex quadrilateral $ABCD$ intersect each other at point $M$. Let positive integers $a$, $b$, $c$ and $d$ be the areas of the resulting triangles $ABM$, $BCM$, $CDM$ and $DAM$, respectively. $a)$ Prove that the product $a\cdot b\cdot c\cdot d$ is a perfect square. $b)$ Suppose that there are exactly two distinct odd primes among $a$, $b$, $c$ and $d$. Find the values of $a$, $b$, $c$ and $d$ such that the area of the quadrilateral $ABCD$ is the smallest possible perfect square.