High-resolution infrared spectra ( \lambda / \Delta \lambda = 50,000 ) have been obtained for twelve red-giant members of the Large Magellanic Cloud ( LMC ) with the Gemini South 8.3m telescope plus Phoenix spectrometer . Two wavelength regions , at 15540Å and 23400Å , were observed . Quantitative chemical abundances of carbon ( both ^ { 12 } C and ^ { 13 } C ) , nitrogen , and oxygen were derived from molecular lines of CO , CN , and OH , while sodium , scandium , titanium , and iron abundances were obtained from neutral atomic lines . The twelve LMC red giants span a metallicity range from [ Fe/H ] = -1.1 to -0.3 . It is found that values for both [ Na/Fe ] and [ Ti/Fe ] in the LMC giants fall below their corresponding Galactic values ( at these same [ Fe/H ] abundances ) by about \sim 0.1 to 0.5 dex ; this effect is similar to abundance patterns found in the few dwarf spheroidal galaxies with published abundances . The program red giants all show evidence of first dredge-up mixing of material exposed to the CN-cycle , i.e . low ^ { 12 } C/ ^ { 13 } C ratios , and lower ^ { 12 } C- with higher ^ { 14 } N-abundances . The carbon and nitrogen trends are similar to what is observed in samples of Galactic red giants , although the LMC red giants seem to show smaller ^ { 12 } C/ ^ { 13 } C ratios for a given stellar mass . This relatively small difference in the carbon isotope ratios between LMC and Galactic red giants could be due to increased extra mixing in stars of lower metallicity , as suggested previously in the literature . Comparisons of the oxygen to iron ratios in the LMC and the Galaxy indicate that the trend of [ O/Fe ] versus [ Fe/H ] in the LMC falls about 0.2 dex below the Galactic trend . Such an offset can be modeled as due to an overall lower rate of supernovae per unit mass in the LMC relative to the Galaxy , as well as a slightly lower ratio of supernovae of type II to supernovae of type Ia .