  While the hunt for new states beyond the standard model (SM) goes on for
various well motivated theories, the leptoquarks are among the most appealing
scenarios at recent times due to a series of tensions observed in $B$-meson
decays. We consider $SU(2)$ singlet and triplet scalar leptoquarks separately,
which contribute to charged and neutral current $B$-meson decays. Focusing on
the single production of these two scalar leptoquarks, we perform a
PYTHIA-based simulation considering all the dominant SM backgrounds at the
current and future setups of the Large Hadron Collider (LHC). The mono-$b$-jet
+ $\ptmiss$ finalstate gives the strongest signal for the singlet leptoquark at
the 30 TeV LHC or Future Circular Collider (FCC), with a possibility of
$5\sigma$ signal significance with $\gtrsim 1000$ \fbi of integrated
luminosity, for the chosen benchmark scenarios. The finalstate consisting of a
$c$-jet and two $\tau$-jets provides highest reach for the singlet leptoquark,
probing an $\mathcal{O}(10^{-1})$ value of the Yukawa-type couplings for up to
$3.0$ TeV leptoquark mass. For the triplet leptoquark, $1-{\rm jet}+2\mu +
\ptmiss$ topology is the most optimistic signature at the LHC, probing
leptoquark couplings to fermions at $\mathcal{O}(10^{-1})$ value for the
leptoquark mass range up to $ 4.0$ TeV. The invariant mass edge distribution is
found to be instrumental in determination of the leptoquark mass scale at the
LHC. We also perform the analysis at the proposed multi-TeV muon collider,
where an $\mathcal{O}(10^{-1})$ leptoquark Yukawa coupling can be probed for a
$5.0$ TeV leptoquark mass.
