Leptoquark Production and Identification in High Energy mu^+ mu^-, e^+ e^- and e gamma Collisions

We study single leptoquark production in $e^+e^-$, $e\gamma$, and $\mu^+\mu^-$ collisions due to the quark content of the photon. Leptoquarks can be produced in substantial numbers for masses very close to the centre of mass energy of the collider which results in equivalently high discovery limits. Using polarization asymmetries in an $e\gamma$ collider the ten different types of leptoquarks listed by Buchm\"uller, R\"uckl and Wyler can be distinquished from one another for leptoquark masses essentially up to the kinematic limit. Thus, if a leptoquark were discovered an $e\gamma$ collider could play a crucial role in determining its origins.