We consider finite sets \(A\subset {\mathbb {Z}}\) that tiles the integers by translations. By periodicity, any such tiling is equivalent to a factorization \(A\oplus B={\mathbb {Z}}_M\) of a finite cyclic group. We prove that a tentative characterization of finite tiles proposed by Coven and Meyerowitz holds for all integer tilings of period \(M=(p_ip_jp_k)^2\) , where \(p_i,p_j,p_k\) are distinct primes. This extends our earlier result for odd M.
