  We study the orbits of ultra-faint dwarf galaxies in the combined presence of
the Milky Way and LMC and we find 6 dwarfs which were likely accreted with the
LMC (Car 2, Car 3, Hor 1, Hyi 1, Phe 2, Ret 2), in addition to the SMC,
representing strong evidence of dwarf galaxy group infall. This procedure
depends on the gravitational pull of the LMC, thus allowing us to place a lower
bound on the Cloud's mass of $M_{\rm LMC} > 1.24\times10^{11} M_\odot$. This
mass estimate is validated by applying the technique to a cosmological zoom-in
simulation of a Milky Way-like galaxy with an LMC analogue where we find that
while this lower bound may be overestimated, it will improve in the future with
smaller observational errors. We apply this technique to dwarf galaxies lacking
radial velocities and find that Eri 3 has a broad range of radial velocities
for which it has a significant chance ($> 0.4$) of having being bound to the
Cloud. We study the non-Magellanic classical satellites and find that Fornax
has an appreciable probability of being an LMC satellite if the LMC is
sufficiently massive. In addition, we explore how the orbits of the Milky Way
satellites change in the presence of the LMC and find a significant change for
several objects. Finally, we find that the LMC satellites are slightly smaller
than the Milky Way satellites at a fixed luminosity, possibly due to the
different tidal environments they have experienced.
