Low mass X-ray binaries that have independent distance measurements and show thermonuclear X-ray bursts are ideal sources for constraining the equation of state of neutron star matter. I will introduce our program to systematically measure the distances, masses, and radii of neutron stars in such binaries. We utilize high energy resolution X-ray spectra to measure the ISM column densities to these sources as well as time resolved, high count rate X-ray spectra to study their bursts. I will discuss in detail how the combination of these observations have led to the measurement of the masses and radii of the neutron stars in the low mass X-ray binaries EXO 1745-248, 4U 1608-52, and 4U 1820-30.