  We construct the type-IIB $AdS_4\times K$ supergravity solutions which are
dual to the three-dimensional ${\cal N}=4$ superconformal field theories that
arise as infrared fixed points of circular-quiver gauge theories. These
superconformal field theories are labeled by a triple $(\rho,\hat \rho,L)$
subject to constraints, where $\rho$ and $\hat \rho$ are two partitions of a
number $N$, and $L$ is a positive integer. We show that in the limit of large
$L$ the localized five-branes in our solutions are effectively smeared, and
these type-IIB solutions are dual to the near-horizon geometry of M-theory
M2-branes at a $\mathbb{C}^4/(Z_k\times Z_{\hat k})$ orbifold singularity. Our
IIB solutions resolve the singularity into localized five-brane throats,
without breaking the conformal symmetry. The constraints satisfied by the
triple $(\rho,\hat\rho,L)$, together with the enhanced non-abelian flavour
symmetries of the superconformal field theories, are precisely reproduced by
the supergravity solutions. As a bonus, we uncover a novel type of "orbifold
equivalence" between different quantum field theories and provide quantitative
evidence for this equivalence.
