Question 131

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?

Name: 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?
Uploaded: 2026-04-04T14:32:08.617146+05:30
Duration: 2 min 26 s
Description: 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?

Solution

Let the no. be x
LCM(x,990) = 6930
6930=$$2\times3^2\times5\times7\times11$$
990=$$2\times3^2\times5\times11$$
Factor of 7 is missing in 990, so x has to be multiple of 7.
x=7a
GCD(x,550)=110
x=110b
x=7a=110b. So, x=770k
Least value of x is 770.
Sum of digits of 770=7+7+0=14
Option B is the answer.