We report on our search for microlensing towards the Large Magellanic Cloud (LMC). Analysis of 5.7 years of photometry on 11.9 million stars in the LMC reveals 13 - 17 microlensing events. This is significantly more than the $sim$ 2 to 4 events expected from lensing by known stellar populations. The timescales ($that$) of the events range from 34 to 230 days. We estimate the microlensing optical depth towards the LMC from events with $2 < that < 400$ days to be 1.2 ^{+0.4}_ {-0.3} ten{-7}$, with an additional 20% to 30% of systematic error. The spatial distribution of events is mildly inconsistent with LMC/LMC disk self-lensing, but is consistent with an extended lens distribution such as a Milky Way or LMC halo. Interpreted in the context of a Galactic dark matter halo, consisting partially of compact objects, a maximum likelihood analysis gives a MACHO halo fraction of 20% for a typical halo model with a 95% confidence interval of 8% to 50%. A 100% MACHO halo is ruled out at the 95% C.L. for all except our most extreme halo model. Interpreted as a Galactic halo population, the most likely MACHO mass is between $ 0.15 msun$ and $ 0.9 msun$, depending on the halo model, and the total mass in MACHOs out to 50 kpc is found to be 9+4-3 10^{10} msun, independent of the halo model. These results are marginally consistent with our previous results, but are lower by about a factor of two. Besides a larger data set, this work also includes an improved efficiency determination, improved likelihood analysis, and more thorough testing of systematic errors, especially with respect to the treatment of potential backgrounds to microlensing, such as supernovae in galaxies behind the LMC. [Abridged]
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