The thermoacoustic modes of a full scale industrial gas turbine combustor have been predicted numerically. The predictive approach combines low order network modelling of the acoustic waves in a simplified geometry, with a weakly nonlinear flame describing function, obtained from incompressible large eddy simulations of the flame region under upstream forced velocity perturbations, incorporating reduced chemistry mechanisms. Two incompressible solvers, each employing different numbers of reduced chemistry mechanism steps, are used to simulate the turbulent reacting flowfield to predict the flame describing functions. The predictions differ slightly between reduced chemistry approximations, indicating the need for more involved chemistry. These are then incorporated into a low order thermoacoustic solver to predict thermoacoustic modes. For the combustor operating at two different pressures, most thermoacoustic modes are predicted to be stable, in agreement with the experiments. The predicted modal frequencies are in good agreement with the measurements, although some mismatches in the predicted modal growth rates and hence modal stabilities are observed. Overall, these findings lend confidence in this coupled approach for real industrial gas turbine combustors.