  In this work, we have explored the sensitivity of multilepton final states in
probing the gaugino sector of R-parity violating supersymmetric scenario with
specific lepton number violating trilinear couplings ($\lambda_{ijk}$) being
non-zero. The gaugino spectrum is such that the charged leptons in the final
state can arise from the R-parity violating decays of the lightest
supersymmetric particle (LSP) as well as R-parity conserving decays of the
next-to-LSP (NLSP). Apart from a detailed cut-based analysis, we have also
performed a machine learning-based analysis using boosted decision tree
algorithm which provides much better sensitivity. In the scenarios with
non-zero $\lambda_{121}$ and/or $\lambda_{122}$ couplings, the LSP pair in the
final states decays to $4l~(l = e, \mu) + \rm E{\!\!\!/}_T$ final states with
$100\%$ branching ratio. We have shown that under this circumstance, a final
state with $\ge 4l$ has the highest sensitivity in probing the gaugino masses.
We also discuss how the sensitivity can change in the presence of $\tau$
lepton(s) in the final state due to other choices of trilinear couplings. We
present our results through the estimation of the discovery and exclusion
contours in the gaugino mass plane for both the HL-LHC and the HE-LHC. For
$\lambda_{121}$ and/or $\lambda_{122}$ nonzero scenario, the projected
2$\sigma$ exclusion limit on NLSP masses reaches upto 2.37 TeV and 4 TeV for
the HL-LHC and the HE-LHC respectively by using a machine learning based
algorithm. We obtain an enhancement of $\sim$ 380 (190) GeV in the projected
2$\sigma$ exclusion limit on the NLSP masses at the 27 (14) TeV LHC.
Considering the same final state ($N_l \geq 4$) for $\lambda_{133}$ and/or
$\lambda_{233}$ non-zero scenario, we find that the corresponding 2$\sigma$
projected limits are $\sim$ 1.97 TeV and $\sim$ 3.25 TeV for the HL-LHC and
HE-LHC respectively.
