  We study the many-body ground states of three-component quantum particles in
two prototypical topological lattice models under strong intercomponent and
intracomponent repulsions. At band filling $\nu=3/4$ for hardcore bosons, we
demonstrate the emergence of three-component fractional quantum Hall (FQH)
effect characterized by the $\mathbf{K}$ matrix, through exact diagonalization
study of four-fold quasidegenerate ground states with a robust spectrum gap and
the combined density-matrix renormalization group calculation of fractional
drag charge pumping. Further we formulate the topological characterization of
FQH states of three-component Bose-Fermi mixtures at various fillings by the
$\mathbf{K}$ matrix. At last we discuss the possible generalization of our
approach to identify non-Abelian three-component spin-singlet FQH states.
