The median number of children is \(\boxed{2}\).
\(100 = 2^2 \times 5^2\)
\(250 = 2 \times 5^3\)
The LCM is the product of the highest powers of all prime factors present in the numbers.
In this case, the prime factors are 2 and 5.
The highest power of 2 is \(2^2\).
The highest power of 5 is \(5^3\).
Therefore, LCM(100, 250) = \(2^2 \times 5^3 = 4 \times 125 = 500\)
The least common multiple of 100 and 250 is \(\boxed{500}\).