Let p be the smallest number, which when added to 2000 makes

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Let p 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 p is

1. 7
2. 5
3. 6
4. 4

Correct Option: A

We find the LCM of 12 , 16 , 18 and 21

∴ LCM = 2 × 2 × 3 × 4 × 3 × 7 = 1008
2 Multiple of 1008 = 1008 × 2 = 2016
∴ Required number = 2016 – 2000 = 16 = p
∴ Sum of digits of p = 1 + 6 = 7