Question : What is the smallest three-digit number which, when divided by 8 or 6, leaves a remainder of 1 in each case?
Option 1: 121
Option 2: 119
Option 3: 123
Option 4: 125
Correct Answer: 121
Solution :
Given,
The smallest 3-digit number leaves 1 remainder when divided by 8 or 6.
8 = 2 × 2 × 2
6 = 3 × 2
⇒ LCM of 8 and 6 = 2 × 2 × 2 × 3 = 24
When we divide 100 by 24, we get 4 as the remainder
The smallest three-digit number which is divisible by 8 or 6 = 100 – 4 + 24 = 120
The smallest three-digit number, when divided by 8 or 6 leaves the remainder 1 in each case
= (120 + 1) = 121.
Hence, the correct answer is 121.
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