  Gamma-proton collisions allow unprecedented investigations of the low x and
high $Q^{2}$ regions in quantum chromodynamics. In this paper, we investigate
the luminosity for "ILC"$\times$LHC ($\sqrt{s_{ep}}=1.3$ TeV) and
"CLIC"$\times$LHC ($\sqrt{s_{ep}}=1.45$ TeV) based $\gamma p$ colliders. Also
we determine the laser properties required for high conversion efficiency.
