In this work, we demonstrate the broadband scattering of light waves incident on coupled silicon nanocylinders. First, it is shown that both electric and magnetic resonances are observed in a single silicon nanocylinder. By using two silicon nanocylinders, we next construct a silicon nanodimer. Thereafter, the original electric and magnetic resonances of the single nanocylinder shift and form hybrid resonant modes in the dimer; meanwhile, a new magnetic resonant mode emerges at a longer wavelength. Consequently, the silicon nanodimer exhibits a broadband scattering response that originates from optically magnetic interactions between dimeric silicon nanocylinders. Furthermore, the scattering bandwidth further increases upon using a silicon nanotrimer. This broadband optical response in silicon nanocylinders is demonstrated via their scattering spectra, and the magnetic interaction is verified by examining the spatial distributions of electromagnetic fields and the retrieved permittivity and permeability of the nanocylinders system. This theoretical finding may provide an approach to realize silicon-based broadband nanoantennas and nanosensors.