Data Sufficiency

A school administrator will assign each student in
a group of n students to one of m classrooms. If
3 < m < 13 < n, is it possible to assign each of the
n students to one of the m classrooms so that each
classroom has the same number of students assigned
to it?
(1) It is possible to assign each of 3n students to
one of m classrooms so that each classroom
has the same number of students assigned to it.
(2) It is possible to assign each of 13n students to
one of m classrooms so that each classroom
has the same number of students assigned to it.

This is from OG 12, Q128.

OA is B. But It is not easy to understand. Someone please help.

n students, m rooms
3 < m < 13 < n
n/m ??

A) 3n/m is integer. insufficient.
if n/m = 16/6, not integer. but 3n/m is integer
if n/m = 16/4, integer, 3n/m also intger

B) 13n/m is integer. m<13 and 13 is integer. thus n/m is also integer.
IMO B

cans wrote:n students, m rooms
3 < m < 13 < n
n/m ??

A) 3n/m is integer. insufficient.
if n/m = 16/6, not integer. but 3n/m is integer
if n/m = 16/4, integer, 3n/m also intger

B) 13n/m is integer. m<13 and 13 is integer. thus n/m is also integer.
IMO B

@ Cans, That means the solution is possible only when we select n which is a multiple of m, we choose.

ex: if m=4, then n can only be 16, 20, etc.,??

Now I seem to be getting close.

Plugging in random numbers for n and m will never work in this problem, or should we first select m and then choose multiples of m as n and plugin??