Question

The least common multiple of a number and 990 is 6930. The greatest common divisor of that number and 550 is 110.
What is the sum of the digits of the least possible value of that number?

• A. 6
• B. 9
• C. 14
• D. 18
• E. None of the remaining options is correct

Answer 1

The Correct Option is C

Step 1: Use the relationship between LCM and GCD. The relationship between LCM and GCD is:

LCM(a, b) ⋅ GCD(a, b) = a ⋅ b

Let the required number be x. Using the given data:

LCM(x, 990) ⋅ GCD(x, 550) = x ⋅ 990.

Substitute:

6,930 ⋅ 110 = x ⋅ 990.

Simplify:

\(x = \frac{6,930 \cdot 110}{990}\)

Step 2: Calculate x. Simplify the expression:

\(x = \frac{6,930 \cdot 110}{990} = \frac{693 \cdot 11}{99} = 77 \cdot 11 = 847.\)

Step 3: Find the sum of the digits of x.

Sum of digits of 847 = 8 + 4 + 7 = 19.

Answer: 19