AMC 8 2017 Problem 24

Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31, 2016. On how many days during the next year did she not receive a phone call from any of her grandchildren? $\textbf{(A) }78 \textbf{(B) }80 \textbf{(C) }144 \textbf{(D) }146 \textbf{(E) }152$