  We report a theoretical study of Feshbach resonances in $^{6}$Li + $^{23}$Na
and $^{7}$Li + $^{23}$Na mixtures at ultracold temperatures using new accurate
interaction potentials in a full quantum coupled-channel calculation. Feshbach
resonances for $l=0$ in the initial collisional open channel $^6$Li$(f=1/2,
m_f=1/2) + ^{23}$Na$(f=1, m_f=1)$ are found to agree with previous
measurements, leading to precise values of the singlet and triplet scattering
lengths for the $^{6,7}$Li$+^{23}$Na pairs. We also predict additional Feshbach
resonances within experimentally attainable magnetic fields for other collision
channels.
