Question : Which is the smallest three-digit number which when increased by 5 becomes divisible by both 2 and 3?
Option 1: 102
Option 2: 105
Option 3: 103
Option 4: 108
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Correct Answer: 103
Solution : Consider the numbers, 102, 103, 105, and 108 ⇒ For 102, When increased by 5, the number becomes 107 which is not divisible by 2. Now, The number = 103 When increased by 5, the number = 108 ⇒ $\frac{108}{2}=54$ and $\frac{108}{3}=36$ Number = 105, when increased by 5, it becomes 110, which is not divisible by 3. Number = 108, when increased by 5, it becomes 113, which is not divisible by 2. Hence, the correct answer is 103.
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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 3: 101
Option 4: 109
Question : Which smallest number must be added to 100, so that the resulting number is completely divisible by 6?
Option 1: 2
Option 2: 3
Option 3: 5
Option 4: 4
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
Question : What is the smallest perfect square number that is divisible by both 10 and 15?
Option 1: 1200
Option 2: 1800
Option 3: 360
Option 4: 900
Question : What is the smallest perfect square which is divisible by both 8 and 12?
Option 1: 100
Option 2: 144
Option 3: 121
Option 4: 196
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