If two positive integers p and q are written as p=a²b³ and q=a³b; a , b are prime number verify

If two positive integers p and q are written as p=a²b³ and q=a³b; a

1.	If two positive integers p and q are written as p=a²b³ and q=a³b; a , b are prime number verify
Answer» LCM(p,q) = a3b3and HCF(p,q) = a2bLCM(p,q)\xa0{tex}\\times{/tex}\xa0HCF(p,q) = a3b3\xa0{tex}\\times{/tex}\xa0a2b{tex}\\begin{array}{l}\\mathrm{LCM}(\\mathrm p,\\mathrm q)\\;\\times\\mathrm{HCF}(\\mathrm p,\\mathrm q)\\;=\\mathrm a^5\\mathrm b^4\\;-----(1)\\\\\\mathrm{and}\\;\\mathrm{pq}=\\mathrm a^2\\mathrm b^3\\;\\times\\mathrm a^3\\mathrm b=\\mathrm a^5\\mathrm b^4\\;------(2)\\\\\\mathrm{from}\\;\\mathrm{eq}^\\mathrm n\\;(1)\\;\\mathrm{and}\\;(2)\\\\\\mathrm{LCM}(\\mathrm p,\\mathrm q)\\;\\times\\mathrm{HCF}(\\mathrm p,\\mathrm q)\\;\\;=\\mathrm{pq}\\\\\\\\\\end{array}{/tex}\xa0