Question

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

• A. $4$
• B. $120$
• C. $121$
• D. $130$

Answer 1

The correct option is C $121$

Since, $123=-1\left(\text{mod}124\right)$

$125=1\left(\text{mod}124\right)$

$127=3\left(\text{mod}124\right)$

Therefore, $123\times 125\times 127=(-1)\left(1\right)\left(3\right)\text{mod}\left(124\right)$

$=-3\text{mod}\left(124\right)$

$=121\text{mod}\left(124\right)$.