What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3?                                                         

                                                 (UPSC CSAT – 2022)

a) 1063

b) 1073

c) 1083

d) 1183

Solution: Ans.(c)

LCM of (6, 9,12, 15, 18) = 180

Smallest multiple of 180 greater than 1000 = 1080

1080 is exactly divisible by all the given numbers but when 1083 is divided by any one of the given number it leaves remainder 3.