Question

If r,s,t are prime numbers and p,q are positive integers such that L.C.M of p, q is $r^2{t}^4{s}^2$. Then the number of ordered pair (p, q) is

• A. 223
• B. 224
• C. 225
• D. 227

Answer 1

The correct option is C 225

$\begin{array}{cc}P& Q\\ r^0& r^2\\ r^1& r^2\\ r^2& r^2\\ r^2& r^0\\ r^2& r^1\end{array}$

Factor r can be distributed in $2\times 3–1$ ways. Similarly
Factor t and S can be distributed in $2\times 5-1$ and $2\times 3-1$ ways
$\therefore$ No. of ordered pairs = $(2.3–1)(2.5–1)(2.3–1)=225$