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
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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