Question

If two positive integers p and q are written as p = a'b' and q = a'b : a,b are prime
numbers, then verify LCM (p,q) HCF(p,q)= pq​

Answer 1

Answer:

Step-by-step explanation:

p = a²b³

q = a³b

HCF ( p,q ) = a²b

[ ∵Product of the smallest power of each

common prime factors in the numbers ]

LCM ( p , q ) = a³b³

[ ∵ Product of the greatest power of each

Now ,

HCF ( p , q ) × LCM ( p , q ) = a²b × a³b³

= a∧5b∧4

And,

pq = a²b³ × a³b

= a∧5 b∧4

.: HCF ( p , q ) × LCM ( p ,q ) = pq

Hence, proved