Problem 22 (2015 AMC 8)

On June $1$, a group of students is standing in rows, with $15$ students in each row. On June $2$, the same group is standing with all of the students in $1$ long row. On June $3$, the same group is standing with just $1$ student in each row. On June $4$, the same group is standing with $6$ students in each row. This process continues through June $12$ with a different number of students per row each day. However, on June $13$, they cannot find a new way of organizing the students. What is the smallest possible number of students in the group?