Question

p is prime number , n is positive integer and n+p=2000 lcm of n and p is 21876. then find n and p
help me

Answer 1

Answer:

11,1989

Step-by-step explanation:

Given that P is a prime number and n is a positive integer.

(i) n + p = 2000.

(ii) np = 21876

 n = (21876/p)

Substitute (ii) in (i), we get

⇒ (21876/p) + p = 2000

⇒ 21876 + p² = 2000p

⇒ p² - 2000p + 21876 = 0

Question Seems to be wrong.

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It should be lcm of n and p is 21879.

Now,

⇒ p² - 2000p + 21879 = 0

⇒ p² - 1989p - 11p + 21879 = 0

⇒ p(p - 1989) - 11(p - 1989) = 0

⇒ (p - 11)(p - 1989) = 0

⇒ p = 11,1989

Given, p is prime number.

So,p = 11 and n = 1989.

Hope it helps!

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