From Dummit Foot, 10.1 ex.11b)
Let M be the abelian group $\mathbb{Z}/\mathbb{24Z}\times \mathbb{Z}/\mathbb{15Z}\times\mathbb{Z}/\mathbb{50Z}$. Let $I=2\mathbb{Z}$ and describe the annihilator I in M as a direct product of cyclic groups.
For reference, If I is a right ideal of R, the annihilator of I in M is $\{m\in M| am=0 ~\forall a\in I \}$
Thanks.