  We have calculated the electroweak O(\alpha) corrections to the processes p p
-> Z \gamma + X -> \nu_l \bar{\nu}_l \gamma + X, p p -> Z \gamma + X -> l
\bar{l} \gamma + X, and p p -> W \gamma + X -> \nu_l \bar{l} \gamma + X at the
LHC, with l=e,\mu and \nu_l=\nu_e,\nu_\mu,\nu_\tau. The virtual corrections are
evaluated in leading-pole approximation, whereas the real corrections are taken
into account exactly. These corrections are implemented into a Monte Carlo
generator which includes both phase-space slicing and subtraction to deal with
soft and collinear singularities. We present numerical results for total cross
sections as well as for experimentally interesting distributions. Applying
typical LHC cuts, the electroweak corrections are of the order of -5% for the
total cross sections and exceed -20% for observables dominated by high
centre-of-mass energies of the partonic processes.
