We study the stochastic dynamics of an arbitrary number of noise-activated cyclic processes, or oscillators, that are all coupled to each other via a dissipative coupling. The N coupled oscillators are described by N phase coordinates driven in a tilted washboard potential. At low N and strong coupling, we find synchronization as well as an enhancement in the average speed of the oscillators. In the large N regime, we show that the collective dynamics can be described through a mean-field theory, which predicts a great enhancement in the average speed. In fact, beyond a critical value of the coupling strength, noise activation becomes irrelevant and the dynamics switch to an effectively deterministic'running'mode. Finally, we study the stochastic thermodynamics of the coupled oscillators, in particular their performance with regards to the thermodynamic uncertainty relation.