  In present study, we search the lambda magic number in hypernuclei within the
framework of relativistic mean field theory (RMF) with inclusion of
hyperon-nucleon and hyperon-hyperon potentials. Based on one- and two-lambda
separation energy and two-lambda shell gap, 2, 8, 14, 18, 20, 28, 34, 40, 50,
58, 68, 70 and 82 are suggested to be the $\Lambda$ magic number within the
present approach. The weakening strength of $\Lambda$ spin-orbit interaction is
responsible for emerging the new lambda shell closure other than the model
scheme. The predicted $\Lambda$ magic numbers are in remarkable agreement with
earlier predictions and hypernuclear magicity quite resembles with nuclear
magicity. %Our results also support the nuclear magicity, Our results are
supported by nuclear magicity, where neutron number N = 34 is experimentally
observed as a magic which is one of the $\Lambda$ closed shell in our
predictions. In addition, the stability of hypernuclei is also examined by
calculating the binding energy per particle, where Ni hypernucleus is found to
be most tightly bound triply magic system in considered hypernuclei. Nucleon
and lambda density distributions are observed and it is found that introduced
$\Lambda$'s have significant impact on total density and reduces the central
depression of the core nucleus. Nucleon and lambda mean field potentials and
spin-orbit interaction potentials are also observed for predicted triply magic
hypernuclei and the addition of $\Lambda$'s affect the both the potentials to a
large extent. The single-particle energy levels are also analyzed to explain
the shell gaps for triply magic multi-$\Lambda$ hypernuclei.
