  We present the results of an ensemble of simulations of the collapse and
fragmentation of dense star-forming cores. We show that even with very low
levels of turbulence the outcome is usually a binary, or higher-order multiple,
system. We take as the initial conditions for these simulations a typical
low-mass core, based on the average properties of a large sample of observed
cores. All the simulated cores start with a mass of $M = 5.4 M_{\odot}$, a
flattened central density profile, a ratio of thermal to gravitational energy
$\alpha_{\rm therm} = 0.45$ and a ratio of turbulent to gravitational energy
$\alpha_{\rm turb} = 0.05 $. Even this low level of turbulence is sufficient to
produce multiple star formation in 80% of the cores; the mean number of stars
and brown dwarfs formed from a single core is 4.55, and the maximum is 10. At
the outset, the cores have no large-scale rotation. The only difference between
each individual simulation is the detailed structure of the turbulent velocity
field. The multiple systems formed in the simulations have properties
consistent with observed multiple systems. Dynamical evolution tends
preferentially to eject lower mass stars and brown dwarves whilst hardening the
remaining binaries so that the median semi-major axis of binaries formed is
$\sim 30$ au. Ejected objects are usually single low-mass stars and brown
dwarfs, yielding a strong correlation between mass and multiplicity. Our
simulations suggest a natural mechanism for forming binary stars that does not
require large-scale rotation, capture, or large amounts of turbulence.
