A homogeneous set of ground-based BVRI observations of ~600 Cepheids is presented to check the Cepheid period-luminosity (PL) zero point for the Large Magellanic Cloud (LMC). The sample of Cepheids is completely self-contained and has been reduced consistently to eliminate photometric differences caused by combining multiple sources of photometry. The Cepheid distances to nearby galaxies obtained by the Hubble Space Telescope (HST) Key Project on the Extragalactic Distance Scale were computed assuming a "standard" PL relation based on a compilation of photoelectric observations of 34 Cepheids and a standard distance modulus to the LMC of 18.50. The final Key Project results substituted a statistically stronger PL relation obtained by the OGLE collaboration. In this paper we compare our data with the OGLE PL relation; the subsample of LMC Cepheids with similar periods to those discovered in the nearby galaxies is fainter at the relevant periods by 0.04+/-0.02mag than the OGLE sample. Substituting in turn this PL relation for that of the OGLE collaboration would raise the Hubble constant by 2%+/-1%, a correction which is not significant. The multicolor data set will also be useful in considering the effects of reddening and chemical composition and deriving an improved Cepheid period-luminosity relation for the LMC.