  The leading order contribution to the shear and bulk viscosities, \eta and
\zeta, of a gluon plasma in perturbative QCD includes the gg -> gg (22)
process, gg <-> ggg (23) process and multiple scattering processes known as the
Landau-Pomeranchuk-Migdal (LPM) effect. Complete leading order computations for
\eta and \zeta were obtained by Arnold, Moore and Yaffe (AMY) and Arnold, Dogan
and Moore (ADM), respectively, with the inelastic processes computed by an
effective g <-> gg gluon splitting. We study how complementary calculations
with 22 and 23 processes and a simple treatment to model the LPM effect compare
with the results of AMY and ADM. We find that our results agree with theirs
within errors. By studying the contribution of the 23 process to \eta, we find
that the minimum angle \theta among the final state gluons in the fluid local
rest frame has a distribution that is peaked at \theta \sim \sqrt{\alpha_{s}},
analogous to the near collinear splitting asserted by AMY and ADM. However, the
average of \theta is much bigger than its peak value, as its distribution is
skewed with a long tail. The same \theta behavior is also seen if the 23 matrix
element is taken to the soft gluon bremsstrahlung limit in the center-of-mass
(CM) frame. This suggests that the soft gluon bremsstrahlung in the CM frame
still has some near collinear behavior in the fluid local rest frame. We also
generalize our result to a general SU(N_c) pure gauge theory and summarize the
current viscosity computations in QCD.
