Question

What is the least number which, when divided by 7, 12 and 15 leaves 1 as the remainder in each case?

• A. 419
• B. 421
• C. 423
• D. 519

Hint:

To solve problems where the remainder is the same for multiple divisors, first find the LCM of the divisors and then add the remainder.

Answer 1

The Correct Option is A

Step 1: Find the Least Common Multiple (LCM).
We need to find the least number which leaves a remainder of 1 when divided by 7, 12, and 15. The required number is of the form \( x = \text{LCM}(7, 12, 15) + 1 \). The LCM of 7, 12, and 15 is calculated as: \[ \text{LCM}(7, 12, 15) = 420. \]

Step 2: Add 1 to the LCM.
Therefore, the required number is: \[ x = 420 + 1 = 419. \]

Final Answer: \[ \boxed{419} \]