The gas turbine engine for an aircraft includes at least a low pressure spool with a low pressure turbine shaft operatively connected to at least one turbine, the low pressure turbine shaft rotatable about an engine axis, and a low pressure compressor operatively connected to a low pressure compressor shaft that is independently rotatable relative to the low pressure turbine shaft. A differential gearbox has an input operatively connected to the low pressure turbine shaft, a first output and a second output, the first output of the differential gearbox operatively connected to the low pressure compressor shaft and the second output of the differential gearbox operatively connected to an output shaft of the gas turbine engine. The differential gearbox permits the output shaft, the low pressure compressor shaft and the low pressure turbine shaft to rotate at different speeds.