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if r,s,t are primes . l.c.m of p,q is{( r^2)(s^4)(t^2)} . then number of possible pairs of (p,q) are -----------

if r,s,t are primes . l.c.m of p,q is{( r^2)(s^4)(t^2)} . then number of possible pairs of (p,q) are -----------

Grade:10

1 Answers

mycroft holmes
272 Points
7 years ago
So p is of the form  and q of the form 
 
Now, if lcm(p,q) =  we need 
 
 
For  we have  or vice versa and thus 5 cases (noting that (2,2) gets counted twice).
 
Similarly for exponents of s, we have 5+5-1 =9 cases, and for exponents of t we have 5 cases.
 
Hence number of possibilities for (p,q) = 5 X 9 X 5 = 225.
 

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