We calculated theoretical evolutionary sequences of asymptotic giant branch (AGB) stars, including the formation and evolution of dust grains in their circumstellar envelopes. By considering stellar populations of the Large Magellanic Cloud (LMC), we calculate synthetic colour-colour and colour-magnitude diagrams, which are compared with those obtained by the Spitzer Space Telescope. The comparison between observations and theoretical predictions outlines that extremely obscured carbon stars and oxygen-rich sources experiencing hot bottom burning (HBB) occupy well-defined, distinct regions in the colour-colour ([3.6] - [4.5], [5.8] - [8.0]) diagram. The C-rich stars are distributed along a diagonal strip that we interpret as an evolutionary sequence, becoming progressively more obscured as the stellar surface layers enrich in carbon. Their circumstellar envelopes host solid carbon dust grains with size in the range 0.05 < a < 0.2 μm. The presence of silicon carbide (SiC) particles is expected only in the more metal-rich stars. The reddest sources, with [3.6] - [4.5] > 2, are the descendants of stars with initial mass Min ˜ 2.5-3 M⊙ in the very latest phases of AGB life. The oxygen-rich stars with the reddest colours ([5.8] - [8.0] > 0.6) are those experiencing HBB, the descendants of ˜5 M⊙ objects formed 108 yr ago; alumina and silicate dust starts forming at different distances from the central star. The overall dust production rate in the LMC is ˜4.5 × 10-5 M⊙ yr-1, the relative percentages due to C and M stars being 85 and 15 per cent, respectively.