We present a method for solving the lightcurve of an eclipsing binary system which contains a Cepheid variable as one of its components as well as the solutions for three eclipsing Cepheids in the Large Magellanic Cloud (LMC). A geometric model is constructed in which the component stars are assumed to be spherical and on circular orbits. The emergent system flux is computed as a function of time, with the intrinsic variations in temperature and radius of the Cepheid treated self-consistently. Fitting the adopted model to photometric observations, incorporating data from multiple bandpasses, yields a single parameter set best describing the system. This method is applied to three eclipsing Cepheid systems from the MACHO Project LMC database: MACHO IDs 6.6454.5, 78.6338.24 and 81.8997.87. A best-fit value is obtained for each systems orbital period and inclination and for the relative radius, color and limb-darkening coefficients of each star. Pulsation periods and parameterizations of the intrinsic color variations of the Cepheids are also obtained and the amplitude of the radial pulsation of each Cepheid is measured directly. The system 6.6454.5 is found to contain a 4.97-day Cepheid, which cannot be definitely classified as Type I or Type II, with an unexpectedly brighter companion. The system 78.6338.24 consists of a 17.7-day, W Vir Class Type II Cepheid with a smaller, dimmer companion. The system 81.8997.87 contains an intermediate-mass, 2.03-day overtone Cepheid with a dimmer, red giant secondary.
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