X is a greatest three-digit number exactly divisible by 12, 20, and 25. The sum of the digits of X is:

Correct option is B

Given:

- We need to find the greatest 3-digit number divisible by 12, 20, and 25.

Formula Used:

- Find the LCM of the given numbers to determine the number that should divide X.

- LCM(12, 20, 25) = LCM $$(2^2 × 3, 2^2 × 5, 5^2) = 2^2 × 3 × 5^2 = 300$$​​

- Now, find the largest 3-digit number divisible by 300 by checking how many times 300 goes into 999.

- Sum of digits can be found once the number is known.

Solution:

LCM of 12, 20, 25 = 300

The greatest 3-digit number is 999.

999 ÷ 300 = 3.33 => Integer part = 3 => 3 × 300 = 900

So, X = 900

Sum of digits of 900 = 9 + 0 + 0 = 9

Final Answer: 9