Does it seems to be similar ??

275625 can be written as ${ 3 }^{ 2 }{ 5 }^{ 4 }{ 7 }^{ 2 }$ . So p and q must be of the form ${ 3 }^{ a }{ 5 }^{ b }{ 7 }^{ c }$ and ${ 3 }^{ x }{ 5 }^{ y }{ 7 }^{ z }$ where either of a or x and c or z is 2, and of b or y is 4 for LCM to be 275625 .

Now let us see choices for a and x . Here, a and x can take 3 values i.e,. 0,1 or 2 . So, number of choices is 3x3 = 9 . But among these choices there are situations where none of them is 3 . So, in these cases a and x can take 2 values i.e., 0 or 1 . So, number of choices where none of a or x is 3 are 2x2 = 4 . Hence , number of choices where either of a and x is 3 are 9 - 4 = 5 .

Similarly, for c and z there are 5 choices.

Now, number of choices for b and y = 5x5 ( total number of choices) - 4x4 (none of b and y is 4) = *25 -16 =9 .

So, by principle of counting number of ordered pairs for p and q are 5x9x5=225