24. Mrs. Sanders has three grandsons who often call her. Among them, one calls her every three days, another every four days, and the third one every five days. It is known that the last time all three called her together was on December 31, 2016. In the following year, she had ( ) days without receiving a call from her grandsons.
(A) 78
(B) 80
(C) 144
(D) 146
(E) 152
24. D.

Let $[x]$ denote the greatest integer not exceeding the real number $x$. By the principle of inclusion-exclusion, we have
$$
\begin{array}{l}
365-\left(\left[\frac{365}{3}\right]+\left[\frac{365}{4}\right]+\left[\frac{365}{5}\right]\right)+ \\
\left(\left[\frac{365}{3 \times 4}\right]+\left[\frac{365}{4 \times 5}\right]+\left[\frac{365}{3 \times 5}\right]\right)- \\
{\left[\frac{365}{3 \times 4 \times 5}\right]} \\
=365-285+72-6=146 .
\end{array}
$$