Co-59 and Li-6,Li-7 MAS NMR has been applied to polytypes O2 and O3 of LiCoO2 at three different magnetic field strengths (4.7, 7.1, and 11.7 T). The Co-59 and Li-6,Li-7 quadrupole and anisotropic shift tensors have been determined by iterative fitting of the NMR line shapes at the three magnetic field strengths. The magnitude of the quadrupole coupling constant at the cobalt site is about 3 times as large for the O2 variety as that for the O3 one. In Li-6,Li-7 NMR, the Li-6,Li-7-Li-6,Li-7 and Li-6,Li-7-Co-59 nuclear dipolar interactions had to be taken into account for a correct determination of the multiple interactions acting on the lithium nuclei. This was conveniently done by using a memory function approach. Calculations of the shift and quadrupole coupling parameters have been performed by using a point dipole and point monopole model, respectively. The shift tenser calculation shows that the magnetic susceptibility in both the O2 and O3 phases is due to Van Vleck paramagnetism for Co3+. In approximation of an ionic crystal, the electric field gradient (EFG) calculation leads to identical point charges at the atomic sites for the two varieties of LiCoO2, and the observed difference in the quadrupole coupling constants results entirely from the fact that the CoO6 octahedra share one face and three edges with the LiO6 octahedra in the O2 phase and six edges in the O3 phase. However, our first principles EFG calculations using the linearized-augmented-plane-wave (LAPW) method were only in qualitative agreement with the experimental data.