  We present the discovery of eight new radio pulsars located in the Large
Magellanic Cloud (LMC). Five of these pulsars were found from reprocessing the
Parkes Multibeam Survey of the Magellanic Clouds, while the remaining three
were from an ongoing new survey at Parkes with a high resolution data
acquisition system. It is possible that these pulsars were missed in the
earlier processing due to radio frequency interference, visual judgment, or the
large number of candidates that must be analysed. One of these new pulsars has
a dispersion measure of 273 pc cm$^{-3}$, almost twice the highest previously
known value, making it possibly the most distant LMC pulsar. In addition, we
present the null result of a radio pulse search of an X-ray point source
located in SNR J0047.2$-$7308 in the Small Magellanic Cloud (SMC). Although no
millisecond pulsars have been found, these discoveries have increased the known
rotation powered pulsar population in the LMC by more than 50%. Using the
current sample of LMC pulsars, we used a Bayesian analysis to constrain the
number of potentially observable pulsars in the LMC to within a 95% credible
interval of 57000$^{+70000}_{-30000}$. The new survey at Parkes is $\sim$20%
complete and it is expected to yield at most six millisecond pulsars in the LMC
and SMC. Although it is very sensitive to short period pulsars, this new survey
provides only a marginal increase in sensitivity to long periods. The limiting
luminosity for this survey is 125 mJy kpc$^2$ for the LMC which covers the
upper 10% of all known radio pulsars. The luminosity function for normal
pulsars in the LMC is consistent with their counterparts in the Galactic disk.
The maximum 1400 MHz radio luminosity for LMC pulsars is $\sim 1000$ mJy
kpc$^2$.
