# Q. What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?

(a) 1012

(b) 1022

(c) 1122

(d) 1222

Correct Answer: (b) 1022

#### Question from UPSC Prelims 2020 CSAT Paper

**Explanation :**

## Number divided by 3,4,5,6

Let’s solve this problem step by step. The least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case can be found using the following method:

First we need to find the least common multiple (LCM) of 3, 4, 5 and 6. The LCM of these numbers is 60.

Now we need to find the smallest four-digit number that is divisible by this LCM. The smallest four-digit number that is divisible by 60 is 1020.

Since we want a remainder of 2 when this number is divided by any of these numbers (3,4,5 and 6), we add 2 to this number.

So the least four-digit number when divided by 3,4,5 and 6 leaves a remainder of 2 in each case is 1020 + 2 =1022.