Optimising the design of aviation propulsion systems using computational fluid dynamics is essential to increase their efficiency and reduce pollutant as well as noise emissions. Nowadays, and within this optimisation and design phase, it is possible to perform meaningful unsteady computations of the various components of a gas-turbine engine. However, these simulations are often carried out independently of each other and only share averaged quantities at the interfaces minimising the impact and interactions between components. In contrast to the current state-of-the-art, this work presents a 360 azimuthal degrees large-eddy simulation with over 2100 million cells of the DGEN-380 demonstrator engine enclosing a fully integrated fan, compressor and annular combustion chamber at takeoff conditions as a first step towards a high-fidelity simulation of the full engine. In order to carry such a challenging simulation and reduce the computational cost, the initial solution is interpolated from stand-alone sectoral simulations of each component. In terms of approach, the integrated mesh is generated in several steps to solve potential machine dependent memory limitations. It is then observed that the 360 degrees computation converges to an operating point with less than 0.5% difference in zero-dimensional values compared to the stand-alone simulations yielding an overall performance within 1% of the designed thermodynamic cycle. With the presented methodology, convergence and azimuthally decorrelated results are achieved for the integrated simulation after only 6 fan revolutions.