Let x be the smallest number which when added to 2000 makes the resulting number divisible by 12 16 ...........

Quantitative Aptitude (CGL) LCM, HCF

Let x be the smallest number, which when added to 2000 makes the resulting number divisible by 12, 16, 18 and 21. The sum of the digits of x is

- We need to find the smallest number \( x \) such that when added to 2000, the sum is divisible by 12, 16, 18, and 21.

- The least common multiple (LCM) of these numbers determines the condition. First, calculate the LCM of 12, 16, 18, and 21.

- The LCM is found to be 1,008.

- Determine \( x \) by finding the smallest positive remainder when subtracting 2000 from a multiple of 1,008.

- Subtract 2000 from the smallest multiple of 1,008 greater than 2000 (i.e., 3024), we get \( x = 1024 \).

- Sum the digits of 1024: \( 1 + 0 + 2 + 4 = 7 \).

- ?? Option 1: 7 is correct.

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