Question

if two positive integers p and q are written as P =A square Bcube and q is equal to A cube B .A B are prime numbers then verify LCM (p,q)* HCF(p,q) is equals to A,B....

Answer 1

LCM (p, q) = a3b3

HCF (p, q) = a2b

LCM (p, q) × HCF (p, q) = a5b4

= (a2b3) (a3b)

= pq

Answer 2

given:p=a square×b cube
q=a cube×b
then LCM=a cube×b cube
HCF=a square×b
to prove:
a×b=LCM(a,b)×HCF(a,b)
therefore,
a square b cube×a cube b=a cube b cube×a squareb
hence
a power 5 ×b power 4=a power 5×b power 4