What is the smallest four-digit number that leaves a remainder of 2 when divided by 3, 4, or 5?

Explanation

The smallest four-digit number is 1000. The least common multiple (LCM) of 3, 4, and 5 is 60. Dividing 1000 by 60 leaves a remainder of 40, so the nearest number divisible by all three is 1000 + (60 - 40) = 1020. Since the required remainder is 2, we add 2 to get 1022, which satisfies the condition.