Question

The least positive remainder when $123 \times 125 \times 127$ is divided by 124 is

• A. 4
• B. 120
• C. 121
• D. 130

Hint:

Reduce each factor modulo the divisor first (using negative residues if convenient), multiply, then convert to the least positive remainder by adding the divisor if negative.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Express each factor modulo 124 and then multiply the residues.
Step 2: Detailed Explanation:
$123 \equiv -1 \pmod{124}$, $\;125 \equiv 1 \pmod{124}$, $\;127 \equiv 3 \pmod{124}$.
Product $\equiv (-1)(1)(3) = -3 \equiv 121 \pmod{124}$.
Step 3: Final Answer:
The least positive remainder is $121$.