  We study a class of eight-supercharge little string theories (LSTs) on the
world-volume of $N$ M5-branes with transverse space $\mathbb{S}^{1}\times
(\mathbb{C}^2/\mathbb{Z}_M)$. These M-brane configurations compactified on a
circle are dual to $M$ D5-branes intersecting $N$ NS5-branes on
$\mathbb{T}^2\times \mathbb{R}^{7,1}$ as well as to F-theory compactified on a
toric Calabi-Yau threefold $X_{N,M}$. We argue that the K\"ahler cone of
$X_{N,M}$ admits three regions associated with weakly coupled quiver gauge
theories of gauge groups $[U(N)]^M, [U(M)]^N$ and $[U(\frac{NM}{k})]^k$ where
$k=\mbox{gcd}(N,M)$. These provide low-energy descriptions of different LSTs.
The duality between the first two gauge theories is well known and is a
consequence of the S-duality between D5- and NS5-branes or the T-duality of the
LSTs. The triality involving the third gauge theory is new and we demonstrate
it using several examples. We also discuss implications of this triality for
the W-algebras associated with the Alday-Gaiotto-Tachikawa dual theories.
