The students of a school can be arranged exactly in rows of 6, of 8 or of 10. The number of students is also a perfect square. What is the least possible number of students?

Explanation

1. 01

   The number is a multiple of $\operatorname{LCM}(6, 8, 10) = 120 = 2^3 \times 3 \times 5$.

2. 02

   For a perfect square every prime needs an even power: raise to $2^4 \times 3^2 \times 5^2$.

3. 03

   That is $120 \times 30 = 3{,}600 = 60^2$.