CSAT 2020

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 :

Let’s solve this problem step by step:

Finding the least four-digit number with remainder 2 when divided by 3, 4, 5, and 6

STEP 1: Find the LCM of 3, 4, 5, and 6
– First, we need the least common multiple (LCM) of 3, 4, 5, and 6
– The LCM of these numbers is 60

STEP 2: Find the smallest four-digit number divisible by LCM
– We need to find the smallest four-digit number divisible by 60
– The smallest four-digit number divisible by 60 is 1020

STEP 3: Add remainder
– Since we want remainder 2 when divided by 3, 4, 5, and 6
– We add 2 to our number: 1020 + 2 = 1022

ANSWER: 1022 is the least four-digit number that leaves remainder 2 when divided by 3, 4, 5, and 6

VERIFICATION:
1022 ÷ 3 = 340 remainder 2
1022 ÷ 4 = 255 remainder 2
1022 ÷ 5 = 204 remainder 2
1022 ÷ 6 = 170 remainder 2

Check Demo Video

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