Lalremsiami buys square tiles in boxes of 2,880 each. What is the least number of boxes she must use so that all the tiles, with none left over, can be laid out as one complete square?

Explanation

1. 01

   $2{,}880 = 2^6 \times 3^2 \times 5$.

2. 02

   The powers of 2 and 3 are even; only 5 has an odd power.

3. 03

   So she needs 5 boxes: $2{,}880 \times 5 = 14{,}400 = 120^2$ tiles.