We have applied the infrared surface brightness (ISB) technique to derive distances to 13 Cepheid variables in the LMC which have periods from 3-42 days. The corresponding absolute magnitudes define PL relations in VIWJK bands which agree exceedingly well with the corresponding Milky Way relations obtained from the same technique, and are in significant disagreement with the observed LMC Cepheid PL relations, by OGLE-II and Persson et al., in these bands. Our data uncover a systematic error in the p-factor law which transforms Cepheid radial velocities into pulsational velocities. We correct the p-factor law by requiring that all LMC Cepheids share the same distance. Re-calculating all Milky Way and LMC Cepheid distances with the revised p-factor law, we find that the PL relations from the ISB technique both in LMC and in the Milky Way agree with the OGLE-II and Persson et al. LMC PL relations, supporting the conclusion of no metallicity effect on the slope of the Cepheid PL relation in optical/near infrared bands.
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