  We consider D-dimensional Einstein gravity coupled to two U(1) fields and a
dilaton with a scalar potential. We derive the condition that the analytical
AdS black holes with two independent charges can be constructed. Turning off
the cosmological constant, the extremal Reissner-Nordstrom black hole emerges
as the harmonic superposition of the two U(1) building blocks. With the
non-vanishing cosmological constant, our extremal solutions contain the
near-horizon geometry of AdS_2 x R^{D-2} with or without a hyperscaling. We
also obtain the magnetic AdS_{D-2} x Y^2 vacua where Y^2 can be R^2, S^2 or
hyperbolic 2-space. These vacua arise as the fix points of some super
potentials and recover the known supersymmetric vacua when the theory can be
embedded in gauged supergravities. The AdS_{D-2} x R^2 vacua are of particular
interest since they are dual to some quantum field theories at the lowest
Landau level. By studying the embedding of some of these solutions in the
string and M-theory, we find that the M2/M5-system with the equal M2 and M5
charges can intersect with another such M2/M5 on to a dyonic black hole.
Analogous intersection rule applies also to the D1/D5-system. The intersections
are non-supersymmetric but in the manner of harmonic superpositions.
