Summary: Three dimensional free-decaying MHD turbulence is simulated by lattice Boltzmann methods on a spatial grid of \(8000^3\) for low and high magnetic Prandtl number. It is verified that \(\nabla \cdot B = 0\) is automatically maintained to machine accuracy throughout the simulation. Isosurfaces of vorticity and current show the persistence of many large scale structures (both magnetic and velocity) for long times – unlike the velocity isosurfaces of Navier-Stokes turbulence.