Question

If 2 positive integers p and q are written as p=a^2b^3 and q=a^3b; a,b are prime numbers, then verify: LCM(p,q) ×HCF(p,q) = pq

Answer 1

Answer:

good morning ..

Step-by-step explanation:

P=a*a*b*b*b

q=a*a*a*b

As a and b are prime numbers so no further factors

What is common in both=a*a*b= a^2b is HCF(p,q)

What is left in both is =b*b and a

LCM(p,q)=(a*a*b)(b*b)(a)=a^3b^3

HCF*LCM=(a^2b)*(a^3b^3)=a^5b^4

p*q=(a^2b^3)(a^3b)=a^5b^4

hope it helps..