If every pair from among the equations $x^2 + px + qr = 0$, $x^2 + qx + rp = 0$ and $x^2 + rx + pq = 0$ has a common root, then the product of the three common roots is ______.

Let the common roots be $\alpha,\beta,\gamma$ respectively. From the first equation, common root $\alpha$ satisfies $\alpha^2 + p\alpha + qr = 0$ Similarly, $\alpha^2 + q\alpha + rp = 0$ Subtracting, $(p-q)\alpha + (qr-rp)=0$ $\Rightarrow (p-q)(\alpha - r)=0$ So $\alpha = r$. Similarly, $\beta = p$ and $\gamma = q$. Hence product of the three common roots $= pqr$