Correct Answer - Option 3 : 3031
Given :
When a number is divided by 12, 16, 18 and 21 it will leave a remainder of 7 in each case.
Concept used :
LCM is the smallest common number that is divided by all numbers given.
Calculations :
12 = 2 × 2 × 3 = 22 × 3
16 = 2 × 2 × 2 × 2 = 24
18 = 3 × 3 × 2 = 32 × 2
21 = 3 × 7
LCM of 12, 16, 18 and 21 = 24 × 32 × 7
⇒ 16 × 9 × 7
⇒ 144 × 7
⇒ 1008
So the number that will leave remainder 7 = 1008k + 7 (where k = 0, 1, 2, 3, 4........)
3rd smallest number of this type = 1008 × 3 + 7
⇒ 3031
∴ Option 3 will be the correct choice.
