By fitting high-quality and simultaneous multiwavelength spectral energy distributions at multiple epochs with a one-zone leptonic jet model, we study the jet properties of three famous blazars: Mrk 421, 3C 454.3 and 3C 279. In the jet model, the emitting electron energy distributions are calculated by solving the kinetic equations of electron injection, escape, adiabatic and radiative energy losses. To explore multidimensional parameter space systematically, we employ a Markov chain Monte Carlo fitting technique. The properties of the emission regions we have derived here are consistent with those in previous studies, for example, the particle-dominated and low-magnetization jet. The new finding is that there is a tight correlation between gamma-ray luminosity and electron injection power and an anticorrelation between gamma-ray luminosity and the jet magnetization parameter. The results suggest that the same energy-dissipative mechanism (such as a shock) could be operating in the jets of different types of blazars, and that the origin of gamma-ray flares is associated with the particle acceleration process.