Magnetohydrodynamical (MHD) dynamos emerge in many different astrophysical situations where turbulence is present, but the interaction between large-scale dynamos (LSDs) and small-scale dynamos (SSDs) is not fully understood. We performed a systematic study of turbulent dynamos driven by isotropic forcing in isothermal MHD with magnetic Prandtl number of unity, focusing on the exponential growth stage. Both helical and nonhelical forcing was employed to separate the effects of LSD and SSD in a periodic domain. Reynolds numbers (ReM) up to similar to 250 were examined and multiple resolutions used for convergence checks. We ran our simulations with the Astaroth code, designed to accelerate 3D stencil computations on graphics processing units (GPUs) and to employ multiple GPUs with peer-to-peer communication. We observed a speedup of approximate to 35 in single-node performance compared to the widely used multi-CPU MHD solver Pencil Code. We estimated the growth rates from both the averaged magnetic fields and their power spectra. At low ReM LSD growth dominates, but at high ReM SSD appears to dominate in both helically and nonhelically forced cases. Pure SSD growth rates follow a logarithmic scaling as a function of ReM. Probability density functions of the magnetic field from the growth stage exhibit SSD behavior in helically forced cases even at intermediate ReM. We estimated mean field turbulence transport coefficients using closures like the second-order correlation approximation (SOCA). They yield growth rates similar to the directly measured ones and provide evidence of a quenching. Our results are consistent with the SSD inhibiting the growth of the LSD at moderate ReM, while the dynamo growth is enhanced at higher ReM.