For multicomponent multiple phases to be in equilibrium at the same pressure and temperature, the __________ of each component must be same in all phases.

Both the chemical potential and fugacity must be same in all the phases to attain thermodynamic equilibrium. Actually, the calculation of chemical potential and visualizing it physically is slightly tedious so, we introduced the concept of fugacity which is easy to visualize and we have also many correlations to measure it so, the origin of fugacity taken place. And we related the chemical potential with it as following:
$${\mu _i} = RTdln{f_i}$$
So, the equality of chemical potential will result in equality of fugacity also between the phases.