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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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 greatest four-digit number which when divided by 3 and 4 leaves remainder 2 in each case?
Option 1: 9994
Option 2: 9996
Option 3: 9998
Option 4: 9995
Question : What is the least number which when divided by 18, 24, and 36 leaves 3 as a remainder in each case?
Option 1: 75
Option 2: 93
Option 3: 111
Option 4: 99
Question : Find the second smallest number which, when divided by 81 or 63, leaves a remainder of 7 in each case.
Option 1: 1246
Option 2: 1141
Option 3: 1362
Option 4: 1137
Question : Which is the smallest three-digit number which when increased by 5 becomes divisible by both 2 and 3?
Option 1: 102
Option 3: 103
Option 4: 108
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