Multi-particle cumulants and corresponding Fourier harmonics are measured for azimuthal angle distributions of charged particles in $pp$ collisions at $\sqrt{s}$ = 5.02 and 13?TeV and in $p$ ?+?Pb collisions at $\sqrt{s_{_\text {NN}}}$ = 5.02?TeV, and compared to the results obtained for low-multiplicity $\mathrm{Pb}~+~\mathrm{Pb}$ collisions at $\sqrt{s_{_\text {NN}}}$ = 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 $\mathrm{Pb}~+~\mathrm{Pb}$ 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 $\mathrm{Pb}~+~\mathrm{Pb}$ , smaller in $p$ ?+?Pb and smallest in $pp$ collisions. The $pp$ results show no dependence on the collision energy, nor on the
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