Suppose $a$, $b$ and $c$ are integers such that the greatest common divisor of $x^2 ax b$ and $x^2 bx c$ is $x 1$ (in the set of polynomials in $x$ with integer coefficients), and the least common multiple of $x^2 ax b$ and $x^2 bx c$ is $x^3-4x^2 x 6$. Find $a b c$.