Let be the Ramsey number of an ‐uniform loose cycle of length versus an ‐uniform clique of order . Kostochka et al. showed that for each fixed , the order of magnitude of is up to a polylogarithmic factor in . They conjectured that for each we have . We prove that , and more generally for every that . We also prove that for every and , if is odd, which improves upon the result of Collier‐Cartaino et al. who proved that for every and we have .