Context : Aims : From the early days in \gamma -ray astronomy , locating the origin of GeV emission within the core of an active galactic nucleus ( AGN ) persisted as an open question ; the problem is to discern between near- and far-site scenarios with respect to the distance from the super massive central engine . We investigate this question under the light of a complete sample of low synchrotron peak ( LSP ) blazars which is fully characterized along many decades in the electromagnetic spectrum , from radio up to tens of GeV . We consider the high-energy emission from bright radio blazars and test for synchrotron self-Compton ( SSC ) and external Compton ( EC ) scenarios in the framework of localizing the \gamma -ray emission sites . Given that the inverse Compton ( IC ) process under the EC regime is driven by the abundance of external seed photons , these photons could be mainly ultraviolet ( UV ) to X-rays coming from the accretion disk region and the broad-line region ( BLR ) , therefore close to the jet launch base ; or infrared ( IR ) seed photons from the dust torus and molecular cloud spine-sheath , therefore far from jet launch base . We investigate both scenarios , and try to reveal the physics behind the production of \gamma -ray radiation in AGNs which is crucial in order to locate the production site . Methods : Based on a complete sample of 104 radio-selected LSP blazars , with 37 GHz flux density higher than 1 Jy , we study broadband population properties associated with the nonthermal jet emission process , and test the capability of SSC and EC scenarios to explain the overall spectral energy distribution ( SED ) features . We use SEDs well characterized from radio to \gamma rays , considering all currently available data . The enhanced available information from recent works allows us to refine the study of Syn to IC peak correlations , which points to a particular \gamma -ray emission site . Results : We show that SSC alone is not enough to account for the observed SEDs . Our analysis favors an EC scenario under the Thomson scattering regime , with a dominant IR external photon field . Therefore , the far-site ( i.e. , far from the jet launch ) is probably the most reasonable scenario to account for the population properties of bright LSP blazars in cases modeled with a pure leptonic component . We calculate the photon energy density associated with the external field at the jet comoving frame to be U ^ { \prime } _ { ext } = 1.69 \times 10 ^ { -2 } erg/cm ^ { 3 } , finding good agreement to other correlated works . Conclusions :