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 = 2 3 10 = 2 × 5 12 = 2 2 × 3 18 = 2 × 3 2 So, the LCM of 8, 10, 12, and 18 = 2 3 × 3 2 × 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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