Turbulent flows at very low Mach numbers are numerically investigated using largeeddy simulation (LES). The numerical computations are carried out by solving the viscous conservation equations for compressible fluids. An implicit dual time stepping scheme combined with low Mach number preconditioning and a multigrid acceleration technique is developed for LES. The method is validated for turbulent channel flow at Re τ = 590 and flow across a cylinder at Re = 3900 and different low Mach numbers. The data are compared with numerical and experimental findings from the literature. The computations show an efficiency increase by a factor of up to 60.