Question : What is the least number which when divided by 8, 10, 12, and 18 leaves a remainder of 5 in each case?
Option 1: 397
Option 2: 365
Option 3: 371
Option 4: 408
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Correct Answer: 365
Solution : Prime factorization of 8, 10, 12, and 18: 8 = 23 10 = 2 × 5 12 = 22 × 3 18 = 2 × 32 So, the LCM of 8, 10, 12, and 18 = 23 × 32 × 5 = 360. The least number which when divided by 8, 10, 12, and 18 leaves a remainder of 5 in each case = 360 + 5 = 365. Hence, the correct answer is 365.
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Question : The least number which when divided by 14, 18, and 36 leaves 1 as the remainder in each case is:
Option 1: 250
Option 2: 252
Option 3: 253
Option 4: 251
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 : A number, when divided by 80, leaves a remainder of 20. What is the remainder when the same number is divided by 16?
Option 1: 2
Option 2: 4
Option 3: 6
Option 4: 8
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
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