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?

Let's say the unknown number is x—the LCM of x, 990= 6930.

LCM is the greatest power of a prime number in those two numbers.

Now let's prime factorize 990 and 6930.

990=2*5*11*$$3^2$$

6930=2*$$3^2$$*5*7*11

The number 990 has all the powers of prime numbers, which are also present in 6930, except 7. So, x definitely has to have 7.

Then, it is given that the GCD of x and 550 is 110. So, x has to be a factor of 110. 110 is not a multiple of 7. So, we have to multiply the 110 by 7. That is 770, which is the minimum value of x.

The sum of digits of x is 7+7+0=14