  In order to shed light whether the `even-odd conjecture' (even numbers of
legs will superconduct accompanied by a spin gap while odd ones do not) for
correlated electrons in ladder systems, the pairing correlation is studied for
the Hubbard model on a two- and three-leg ladders. We have employed both the
weak-coupling renormalization group and the quantum Monte Carlo (QMC) method
for strong interactions. For the two-leg Hubbard ladder, a systematic QMC (with
a controlled level spacings) has detected an enhanced pairing correlation,
which is consistent with the weak-coupling prediction. We also calculate the
correlation functions in the three-leg Hubbard ladder and show that the
weak-coupling study predicts the dominant superconductivity, which refutes the
naive even-odd conjecture. A crucial point is a spin gap for only some of the
multiple spin modes is enough to make the ladder superconduct with a pairing
symmetry (d-like here) compatible with the gapped mode. A QMC study for the
three-leg ladder endorses the enhanced pairing correlation.
