  The triple top quark production processes have been investigated and
calculated in the scope of the Standard Model. The cross sections for different
channels are provided for the proton-proton collision energies of $\sqrt{s}=$
14 and 100 TeV. The importance of the electroweak contribution has been
demonstrated. For the main channels the interference between the gluon and the
weak bosons mediated contributions is negative and significant, therefore the
complete set of diagrams has to be taken into account. Estimated total rates
are about 1.9 fb for $\sqrt{s}=14$ TeV and 530 fb for $\sqrt{s}=100$ TeV. A
simple estimation of the uncertainty of the calculated cross sections gives
about 20\%. The integrated luminosity of 3 ab$^{-1}$ at HL-LHC allows expecting
about 5700 events, giving a chance to detect this rare process.
