Washington-system colors of 40 Cepheids in the Large Magellanic Cloud are used to study the metal abundances within the LMC and to compare with abundances in the SMC and the Galaxy. The LMC Cepheids are quite homogeneous: they show a dispersion in observed [A/H] of ±0.14, probably due to a width for the instability strip of about 0m.07 in T1 - T2 (about 400 K) combined with a real dispersion in [A/H] of ±0.1. Neither they nor SMC Cepheids show the correlation of residuals from the P - L relation with abundance which has been predicted based on evolutionary models. The values of reddening found within the LMC are weakly correlated with H I column density, and are sufficiently small [mean E (T1 - T2) = 0m.04] that the derived dust/gas ratio in the LMC is 0.4 times that in the Galaxy. No gradient in abundances within the LMC is found, either with east-west position or radially. It is suggested that variations both in the B/R ratio of supergiants and in the mean periods of Cepheids across the LMC might be better explained by variations in the rate of star formation rather than by abundance variations. The abundances of the LMC and SMC Cepheids relative to Galactic Cepheids are found to be -0.09 and -0.65, respectively, and are compared with results from other studies.