Question

if two positive integer ‘p’&‘q’are written as p=a²b³& q=a³b where a, b are prime numbers prove that LCM (p,q)&LCM (p,q)=p&q

Answer 1

Answer:

Step-by-step explanation:

p=a²b³

q=a³b

LCM (p.q)=a³b³

HCF(p,q)=a²b

Hence LCM (p.q)*HCF (p.q)=a³b³*a²b=a^5b^4

LCM (p.q)*HCF (p.q)=a^5b^4----------------------(1)

Now p*q=a²b³ *a³b

or p*q=a^(2+3)*b^(3+1)=a^5b^4------------------(2)

From (1) and (2) we get

LCM (p.q)*HCF (p.q)=p*q

hence proved