Low Mach problems arise in gas dynamics when the local speed is much smaller than the acoustic waves. In these regimes, a full resolution of all the waves requires very small time steps, while usually one is interested in the slow dynamics of the material wave. In this work, we use a relaxation approach to separate the slow and the fast scales, and integrate the fast scales implicitly. We also prove that we recover the correct asymptotic limit, if the initial data is close to the vanishing Mach limit, which yields the incompressible Euler equations. Joint work with G. Puppo (La Sapienza) and C. Klingenberg (JMU Würzburg).