  We model simultaneous or quasi-simultaneous multi-band spectral energy
distributions (SEDs) for a sample of 25 blazars that have radio core-shift
measurements, where a one-zone leptonic model and Markov chain Monte Carlo
technique are adopted. In the SED fitting for 23 low-synchrotron-peaked (LSP)
blazars, the seed photons from broad line region (BLR) and molecular torus are
considered respectively in the external Compton process. We find that the SED
fitting with the seed photons from the torus are better than those utilizing
BLR photons, which suggests that the $\gamma$-ray emitting region may be
located outside the BLR. Assuming the magnetic field strength in the
$\gamma$-ray emitting region as constrained from the SED fitting follows the
magnetic field distribution as derived from the radio core-shift measurements
(i.e., $B(R)\simeq B_{\rm 1 pc}(R/\rm 1pc)^{-1}$, $R$ is the distance from the
central engine and $B_{\rm 1 pc}$ is the magnetic field strength at 1 pc), we
further calculate the location of the $\gamma$-ray emitting region,
$R_{\gamma}$, for these blazars. We find that
$R_{\gamma}\sim2\times10^{4}R_{\rm S}\simeq10 R_{\rm BLR}$ ($R_{\rm S}$ is the
Schwarzschild radius and $R_{\rm BLR}$ is the BLR size), where $R_{\rm BLR}$ is
estimated from the broad line luminosities using the empirical correlations
obtained using the reverberation mapping methods.
