Question

If p is prime and q is positive integers such that P +Q equal to 1696. If p and q are co prime and their LCM is 21879. Pls answer it fast I please all

Answer 1

Answer:

p and q are 13 and 1683

Step-by-step explanation:

Given:

$p+q=1696$......(1)

since p and q are co prime, their GCD is 1

we know that

$p*q=GCD * LCM$

$\implies\:p*q=1*21879$

$\implies\:p*q=21879$

$\implies\:q=\frac{21879}{p}$...(2)

using (2) in (1) we get

$p+\frac{21879}{p}=1696$

$\frac{p^2+21879}{p}=1696$

$p^2+21879=1696p$

$p^2-1696p+21879=0$

$(p-1683)(p-13)=0$

$p=1683,13$

since p is prime, p=13

$\implies\:q=1683$

$\therefore\:$p and are 13 and 1683