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

Solution :
$$\because $$ $$r, s, t$$  are prime numbers,
∴ Section of $$(p, q)$$  can be done as follows
∴ $$r$$ can be selected 1 + 1 + 3 = 5 ways
\[\begin{array}{l} \begin{array}{*{20}{c}} p\\ {{r^0}}\\ {{r^1}} \end{array}\,\,\,\,\,\,\begin{array}{*{20}{c}} q\\ {{r^2}}\\ {{r^2}} \end{array}\\ \begin{array}{*{20}{c}} {{r^2}}&{{r^0},{r^1},{r^2}} \end{array} \end{array}\]
Similarly $$s$$ and $$t$$ can be selected in 9 and 5 ways respectively .
∴ Total ways $$ = 5 \times 9 \times 5 = 225$$