If $r, s, t$ are prime numbers and $p, q$ are the positive integers such that LCM of $p, q$ is $r^2 s^4 t^2$, then the number of ordered pairs $(p, q)$ is

• A

  252
• B

  254
• Correct answer
  C

  225
• D

  224

Solution

Since, $r, s, t$ are prime numbers. $\therefore$ Selection of $p$ and $q$ are as under
$\therefore$ Total number of ways to select $s=9$. Similarly, the number of ways to select $t=5$. $\therefore$ Total number of ways $=5 \times 9 \times 5=225$.

Hence, the correct answer is option: 'C'.