  It is well known that if a finite set $A\subset\mathbb{Z}$ tiles the integers
by translations, then the translation set must be periodic, so that the tiling
is equivalent to a factorization $A\oplus B=\mathbb{Z}_M$ of a finite cyclic
group. We are interested in characterizing all finite sets $A\subset\mathbb{Z}$
that have this property. Coven and Meyerowitz (1998) proposed conditions (T1),
(T2) that are sufficient for $A$ to tile, and necessary when the cardinality of
$A$ has at most two distinct prime factors. They also proved that (T1) holds
for all finite tiles, regardless of size. It is not known whether (T2) must
hold for all tilings with no restrictions on the number of prime factors of
$|A|$.
  We prove that the Coven-Meyerowitz tiling condition (T2) holds for all
integer tilings of period $M=(p_ip_jp_k)^2$, where $p_i,p_j,p_k$ are distinct
odd primes. The proof also provides a classification of all such tilings.
