MathNet 2012 Question 91

Let $x$, $y$, $z$, $u$, $v$ and $w$ be integers satisfying $x^2 + y^2 = u^2$, $x^2 + z^2 = v^2$ and $y^2 + z^2 = w^2$. Find an integer $\ell$ so that $518000 \lt \ell \lt 518518$ and $\ell$ divides $xyzuvw$.