  We propose a size-consistent Gr\"uneisen-quasiharmonic approach (GQA) to
calculate the lattice thermal conductivity $\kappa_l$ where the Gr\"uneisen
parameters that measure the degree of phonon anharmonicity are calculated
directly using first-principles calculations. This is achieved by identifying
and modifying two existing equations related to the Slack formulae for
$\kappa_l$ that suffer from the size-inconsistency problem when dealing with
non-monoatomic primitive cells (where the number of atoms in the primitive cell
$n$ is greater than one). In conjunction with other thermal parameters such as
the acoustic Debye temperature $\theta_a$ that can also be obtained within the
GQA, we predict $\kappa_l$ for a range of materials taken from the diamond,
zincblende, rocksalt, and wurtzite compounds. The results are compared with
that from the experiment and the quasiharmonic Debye model (QDM). We find that
in general the prediction of $\theta_a$ is rather consistent among the GQA,
experiment, and QDM. However, while the QDM somewhat overestimates the
Gr\"uneisen parameters and hence underestimates $\kappa_l$ for most materials,
the GQA predicts the experimental trends of Gr\"uneisen parameters and
$\kappa_l$ more closely. We expect the GQA with the modified Slack formulae
could be used as an effective and practical predictor for $\kappa_l$,
especially for crystals with large $n$.
