Multi-particle cumulants and corresponding Fourier harmonics are measured for azimuthal angle distributions of charged particles in pp collisions at s = 5.02 and 13 TeV and in p + Pb collisions at sNN = 5.02 TeV, and compared to the results obtained for low-multiplicity Pb+Pb collisions at sNN = 2.76 TeV. These measurements aim to assess the collective nature of particle production. The measurements of multi-particle cumulants confirm the evidence for collective phenomena in p + Pb and low-multiplicity Pb+Pb collisions. On the other hand, the pp results for four-particle cumulants do not demonstrate collective behaviour, indicating that they may be biased by contributions from non-flow correlations. A comparison of multi-particle cumulants and derived Fourier harmonics across different collision systems is presented as a function of the charged-particle multiplicity. For a given multiplicity, the measured Fourier harmonics are largest in Pb+Pb, smaller in p + Pb and smallest in pp collisions. The pp results show no dependence on the collision energy, nor on the multiplicity.