The X-ray luminosity and temperature of clusters and groups of galaxies do not scale in a self-similar manner. This has often been interpreted as a sign that the intracluster medium has been substantially heated by non-gravitational sources. In this paper, we propose a simple model which, instead, uses the properties of galaxy formation to explain the observations. Drawing on available observations, we show that there is evidence that the efficiency of galaxy formation was higher in groups than in clusters. If confirmed, this would deplete the low-entropy gas in groups, increase their central entropy and decrease their X-ray luminosity. A simple, empirical, hydrostatic model appears to match both the luminosity-temperature relation of clusters and properties of their internal structure as well.