  We investigate the constraints on the leptoquark Yukawa couplings and
Higgs-leptoquark quartic couplings for scalar doublet leptoquark $\tilde{R}_2$,
scalar triplet leptoquark $\vec S_3$ and their combination with both three
generations and one generation from perturbative unitarity and vacuum
stability. Perturbative unitarity of all the dimensionless couplings have been
studied via one- and two-loop beta-functions. Introduction of new $SU(2)$
multiplets in terms of these leptoquarks fabricate Landau poles at two-loop
level in the gauge coupling $g_2$ at $10^{19.7}$ GeV and $10^{14.4}$ GeV,
respectively for $\vec S_3$ and $\tilde{R}_2+\vec S_3$ models with three
generations. However, such Landau pole ceases to exist for $\tilde{R}_2$ and
any of these extensions with both one and two generations till Planck scale.
The Higgs-leptoquark quartic couplings acquire severe constraints to protect
Planck scale perturbativity, whereas leptoquark Yukawa couplings get some upper
bound in order to respect Planck scale stability of Higgs Vacuum. The Higgs
quartic coupling at two-loop constraints the leptoquark Yukawa couplings for
$\tilde{R}_2,\vec S_3, \,\tilde{R}_2+\vec S_3$ with values $\lesssim 1.30,
3.90, 1.00$ with three generations. In the effective potential approach, the
presence of any of these leptoquarks with any number of generations pushes the
metastable vacuum of the Standard Model to the stable region.
