We combine variability information from the MAssive Compact Halo Objects (MACHO) survey of the Large Magellanic Cloud (LMC) with infrared photometry from the Spitzer Space Telescope Surveying the Agents of a Galaxys Evolution (SAGE) survey to create a dataset of ~30 000 variable red sources. We photometrically classify these sources as being on the first ascent of the Red Giant Branch (RGB), or as being in one of three stages along the Asymptotic Giant Branch (AGB): oxygen-rich, carbon-rich, or highly reddened with indeterminate chemistry (extreme AGB candidates). We present linear period-luminosity relationships for these sources using 8 separate infrared bands (J, H, K, 3.6, 4.5, 5.8, 8.0, and 24 micron) as proxies for the luminosity. We find that the wavelength dependence of the slope of the period-luminosity relationship is different for different photometrically determined classes of AGB stars. Stars photometrically classified as O-rich show the least variation of slope with wavelength, while dust enshrouded extreme AGB stars show a pronounced trend toward steeper slopes with increasing wavelength. We find that O-rich AGB stars pulsating in the fundamental mode obey a period-magnitude relation with a slope of -3.41 +/- 0.04 when magnitude is measured in the 3.6 micron band, in contrast to C-rich AGB stars, which obey a relation of slope -3.77 +/- 0.05.
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