Question

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

• A. 5
• B. 9
• C. 7
• D. 8

Answer 1

Answer:

B. 9

We’re looking for the greatest three-digit number exactly divisible by 12, 20, and 25, and then the sum of its digits.

Step 1: Find the LCM of 12, 20, and 25

• $(12 = 2^2 \times 3)$

• $(20 = 2^2 \times 5)$

• $(25 = 5^2)$

$\text{LCM} = 2^2 \times 3 \times 5^2 = 300$

Step 2: Find the greatest three-digit multiple of 300

• $(300 \times 3 = 900)$

• $(300 \times 4 = 1200) (not three-digit)$

So, (X = 900)

Step 3: Find the sum of the digits of (X)

$9 + 0 + 0 = \boxed{9}$

Final Answer: 9