If the LCM of is , where are prime numbers and are positive integers, then the number of ordered pair is [2006]

Question

If the LCM of $p, q$ is $r^{2} t^{4} s^{2}$ , where $r, s, t$ are prime numbers and $p, q$ are positive integers, then the number of ordered pair $(p, q)$ is [2006]

Smart Achievers · Accepted Answer

(3)

$∵$ $r^{2} t^{4} s^{2}$

$∴$ $Section of (p, q) can be done as follows$

$∴$ $r can be selected in (1 + 1 + 3 = 5) ways$

$Similarly, t and s can be selected in 9 and 5 ways respectively.$

$∴$ $Total number of ordered pairs (p, q) = 5 \times 9 \times 5 = 225$

Solution

Q.
If the LCM of $p, q$ is $r^{2} t^{4} s^{2}$ , where $r, s, t$ are prime numbers and $p, q$ are positive integers, then the number of ordered pair $(p, q)$ is [2006]

1 252

2 254

3 225

4 224

Ans.
(3)

$∵$ $r, s, t are prime numbers,$

$∴$ $Section of (p, q) can be done as follows$

$∴$ $r can be selected in (1 + 1 + 3 = 5) ways$

$Similarly, t and s can be selected in 9 and 5 ways respectively.$

$∴$ $Total number of ordered pairs (p, q) = 5 \times 9 \times 5 = 225$

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