To find the least number of soldiers that can be drawn up in troops of 12, 15, 18, and 20 soldiers, we need to find the least common multiple (LCM) of these numbers.

The LCM of two numbers is the smallest number that is divisible by both numbers. To find the LCM of more than two numbers, we can follow these steps:

Step 1: Prime factorize each number
Step 2: Write down the prime factors of each number, including any repeated factors
Step 3: Take the highest power of each prime factor from all the numbers
Step 4: Multiply all the prime factors obtained in Step 3 to get the LCM

Let's follow these steps for the given numbers:

Step 1: Prime factorize each number
12 = 2^2 * 3
15 = 3 * 5
18 = 2 * 3^2
20 = 2^2 * 5

Step 2: Write down the prime factors of each number
12: 2, 2, 3
15: 3, 5
18: 2, 3, 3
20: 2, 2, 5

Step 3: Take the highest power of each prime factor
2^2, 3^2, 5

Step 4: Multiply all the prime factors
2^2 * 3^2 * 5 = 4 * 9 * 5 = 180

Therefore, the least number of soldiers that can be drawn up in troops of 12, 15, 18, and 20 soldiers is 180.

However, we also need to find a number that can be arranged in a solid square. A solid square has equal sides, so we need to find a perfect square that is divisible by 180.

The smallest perfect square greater than 180 is 15^2 = 225. However, 225 is not divisible by 180.

The next perfect square is 16^2 = 256. 256 is divisible by 180 because 256/180 = 1 remainder 76.

The next perfect square is 17^2 = 289. 289 is not divisible by 180.

Therefore, the least number of soldiers that can be drawn up in troops of 12, 15, 18, and 20 soldiers and also in the form of a solid square is 256.

Thus, the correct answer is option A) 900.