binomial dbt

If r, s, t are prime numbers and p, q are the positive integers such that the LCM of p, q is r²t⁴s², then the number of ordered pair (p, q) is

(a) 252 (b) 254
(c) 225 (d) 224

1 Answers

Here either q or p should have 2 as the highest power or r, 4 as the highest power of t and 2 as the highest power of s

so the number of ways is {3 x 2-1} x {5 x 2-1} x {3 x 2 -1 } =225

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