  We present a three--pronged numerical approach to the dynamo problem at low
magnetic Prandtl numbers $P_M$. The difficulty of resolving a large range of
scales is circumvented by combining Direct Numerical Simulations, a
Lagrangian-averaged model, and Large-Eddy Simulations (LES). The flow is
generated by the Taylor-Green forcing; it combines a well defined structure at
large scales and turbulent fluctuations at small scales. Our main findings are:
(i) dynamos are observed from $P_M=1$ down to $P_M=10^{-2}$; (ii) the critical
magnetic Reynolds number increases sharply with $P_M^{-1}$ as turbulence sets
in and then saturates; (iii) in the linear growth phase, the most unstable
magnetic modes move to small scales as $P_M$ is decreased and a Kazantsev
$k^{3/2}$ spectrum develops; then the dynamo grows at large scales and modifies
the turbulent velocity fluctuations.
