Question

If p is prime , n is a positive integer and n+p = 2000. Lcm of n and p is . Then find n and p

Answer 1

if n+p = 2000 and LCM of n and p is 2x2x2x2x5x5x5 = 2000

your question is in complete lcm of n and p is nothing so how we find n and p .

Answer 2

Answer:

P is prime and n is a positive integer

P is prime means factor of p is 1 and p

so we can write

n*p=21879 ------> n=21879/p

n+p=2000  ------>n=2000-p

by equating both n

2000 - p = 21879/p

 2000p-p2=21879

 p2 -2000p=-21879

 p2 -2000p + 21879 =0

 (p-11)(p-1989)=0

p=11 and p=1989

 

as 11 is prime no.  

p=11

n= 1989