In this paper, the response behaviors of two parallel structures coupled by Lead Extrusion Dampers (LED) under various earthquake ground motion excitations are investigated. The equation of motion for the two parallel, multi-degree-of-freedom (MDOF) structures connected by LEDs is formulated. To explore the viability of LED to control the responses, namely displacement, acceleration and shear force of parallel coupled structures, the numerical study is done in two parts: (1) two parallel MDOF structures connected with LEDs having same damper damping in all the dampers and (2) two parallel MDOF structures connected with LEDs having different damper damping. A parametric study is conducted to investigate the optimum damping of the dampers. Moreover, to limit the cost of the dampers, the study is conducted with only 50% of total dampers at optimal locations, instead of placing the dampers at all the floor level. Results show that LEDs connecting the parallel structures of different fundamental frequencies, the earthquake-induced responses of either structure can be effectively reduced. Further, it is not necessary to connect the two structures at all floors; however, lesser damper at appropriate locations can significantly reduce the earthquake response of the coupled system, thus reducing the cost of the dampers significantly.