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: Determine the Least Common Multiple (LCM).
Identify the smallest number that yields a remainder of 1 when divided by 7, 12, and 15. This number can be expressed as \( x = \text{LCM}(7, 12, 15) + 1 \).The calculation for the LCM of 7, 12, and 15 is:\[\text{LCM}(7, 12, 15) = 420.\]

Step 2: Increment the LCM by 1.
Consequently, the sought-after number is:\[x = 420 + 1 = 419.\]

Conclusion: \[ \boxed{419} \]