  The eigenstates of an electron in the chiral two-dimensional electron gas
(C2DEG) formed in an AB-stacked bilayer or an ABC-stacked trilayer graphene is
a spinor with $4$ or $6$ components respectively. These components give the
amplitude of the wave function on the $4$ or $6$ carbon sites in the unit cell
of the lattice. In the tight-binding approximation, the eigenenergies are thus
found by diagonalizing a $4\times 4$ or a $6\times 6$ matrix. In the continuum
approximation where the electron wave vector $% k<<1/a_{0},$ with $a_{0}$ the
lattice constant of the graphene sheets, a common approximation is the two-band
model\cite{McCann2006} (2BM)\ where the eigenstates for the bilayer and
trilayer systems are described by a two-component spinor that gives the
amplitude of the wave function on the two sites with low-energy $\left\vert
E\right\vert <<\gamma_{1}$ where $% \gamma_{1}$ is the hopping energy between
sites that are directly above one another in adjacent layers. The 2BM has been
used extensively to study the phase diagram of the C2DEG in a magnetic field as
well as its transport and optical properties. In this paper, we use a numerical
approach to compute the eigenstates and Landau level energies of the full
tight-binding model in the continuum approximation and compare them with the
prediction of the 2BM when the magnetic field or an electrical bias between the
outermost layers is varied. Our numerical analysis shows that the 2BM is a good
approximation for bilayer graphene in a wide range of magnetic field and bias
but mostly for Landau level $M=0.$ The applicability of the 2BM in trilayer
graphene, even for level $M=0,$ is much more restricted. In this case, the 2BM\
fails to reproduce some of the level crossings that occur between the
sub-levels of $M=0.$
