The marching band

Question

A marching band is practicing. When it has rows of 2, there is someone left over. When it has rows of 3 or 4 it also has someone left over. When they form rows of five, they don't have anyone left over. What is the least number of members the marching band can have?

Answer 1

"What is the least number of members the marching band can have?"  means to find the LCM (Least Common Multiple) of:

It is odd -- "rows of 2, there is someone left over"       1  3  5  7  9  11  13  15  17  19  21  23  25  27  ...

"Rows of 3 with 1 left over"                                         4  7  10   13   16   19   22   25   28   31   ...

"Rows of 4 with 1 left over"                                         5   9   13   17   21  25   29   33  ...

"Rows of 5 with none left over"                                    5   10   15   20   25   30   35   ...

 

The least number of members the marching band can have is 25 (lowest, in all the lists).

 

Check:

     Rows of 2:    25/2 = 12 with 1 left over

     Rows of 2:    25/3 = 8 with 1 left over

     Rows of 4:    25/4 = 6 with 1 left over

     Rows of 5:    25/5 = 5 with none left over