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In this paper we refine our method for the abundance analysis of highresolution spectroscopy of the integrated light of unresolved globular clusters(GCs). This method was previously demonstrated for the analysis of old ($>$10Gyr) Milky Way GCs. Here we extend the technique to young clusters using atraining set of 9 GCs in the Large Magellanic Cloud (LMC). Depending on thesignal-to-noise ratio of the data, we use 20-100 Fe lines per cluster tosuccessfully constrain the ages of old clusters to within a $\sim$5 Gyr range,the ages of $\sim$2 Gyr clusters to a 1-2 Gyr range, and the ages of theyoungest clusters (0.05-1 Gyr) to a $\sim$200 Myr range. We also demonstratethat we can measure [Fe/H] in clusters with any age less than 12 Gyrs withsimilar or only slightly larger uncertainties (0.1-0.25 dex) than thoseobtained for old Milky Way GCs (0.1 dex); the slightly larger uncertainties aredue to the rapid evolution in stellar populations at these ages. In this paper,we present only Fe abundances and ages. In the next paper in this series, wepresent our complete analysis of the $\sim 20$ elements for which we are ableto measure abundances. For several of the clusters in this sample, there are nohigh resolution abundances in the literature from individual member stars; ourresults are the first detailed chemical abundances available. The spectra usedin this paper were obtained at Las Campanas with the echelle on the du PontTelescope and with the MIKE spectrograph on the Magellan Clay Telescope.

Globular Cluster Abundances from High-Resolution, Integrated-Light Spectroscopy. III. The Large Magellanic Cloud: Fe and Ages