Question

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

• A. 252
• B. 254
• C. 225
• D. 224

Answer 1

The correct option is C 225

If L.C.M. of p and q is $r^2{t}^4{s}^2$ then distribution of factors r is as follows:

Thus, factor r can be distributed in $2\times 3-1$ ways. Similarly,
factors t and s can be distributed in $2\times 5-1$ and $2\times 3-1$ ways,
respectively.
Hence, number of ordered pairs are $(2\times 3-1)\times (2\times 5-1)\times (2\times 3-1)=225$