Current hybrid computational aeroacoustic methodologies for broadband noise prediction rely on large eddy simulation (LES) for noise source computation, and integral methods for noise propagation. In this paper, LES of a benchmark controlled-diffusion airfoil was conducted, utilizing the rotation rate based Smagorinsky model (RoSM). The RoSM is seen to provide flow results of equal or improved accuracy as compared to the dynamic Smagorinsky model, with 35% less computational cost, with computational benefits of the RoSM increasing with mesh size. Current integral methods for noise propagation, including Formulation 1A of Farassat, require numerical differentiation of highly turbulent input flow data coming from LES, introducing numerical inaccuracies. Here, Formulation 1 of Farassat is modified to entirely avoid the numerical differentiation of flow field data. The ability of the methodology for broadband noise prediction is demonstrated, with the prediction at high frequencies being considerably closer to experimental data than Formulation 1A. For low discrete frequency noise prediction, Formulation 1A is still recommended. The use of two innovative approaches in conjunction for broadband noise prediction is seen to be efficient and easy to implement, without compromising on accuracy.