Question

If two positive integers p&q are written as p=a²b³andq=a³b;a and b are the prime numbers then Virify LCM (p,q)×HCF(p,q)=pq

Answer 1

p=

$a ^{2} \times b ^{3}$

q=

${a}^{3} \times b$

so the HCF will be

${a}^{2} \times b$

and LCM will be

${a}^{3} \times {b}^{3}$

so we know that LCM×HCF=p×q

${a}^{3} \times {b}^{3} \times {a}^{2} \times b = {a}^{2} \times {b}^{3} \times {a}^{3} \times b$

this will be

${a}^{5} \times {b}^{4} = {a}^{5} \times {b}^{4}$

Hence proved