Question : What is the smallest three-digit number when divided by 2, 3, and 4 leaving the remainder 1 in each case?
Option 1: 111
Option 2: 105
Option 3: 101
Option 4: 109
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Correct Answer: 109
Solution : Smallest 3-digit number = 100 LCM of 2, 3, 4 = 12 100 = 12 × 8 + 4 Remainder = 1 $\therefore$ Required number = 100 + (12 – 4) + 1 = 108 + 1 = 109 Hence, the correct answer is 109.
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