Question Number 69567 by Ajao yinka last updated on 25/Sep/19
Commented by Prithwish sen last updated on 25/Sep/19
$$\mathrm{Let}\:\mathrm{us}\:\mathrm{assume}\:\mathrm{gcd}\left(\mathrm{m},\mathrm{n}\right)=\mathrm{1} \\ $$$$\mathrm{then}\:\emptyset\left(\mathrm{mn}\right)=\emptyset\left(\mathrm{m}\right)\emptyset\left(\mathrm{n}\right) \\ $$$$\therefore\:\frac{\emptyset\left(\mathrm{mn}\right)}{\mathrm{gcd}\left(\left(\emptyset\left(\mathrm{m}\right),\emptyset\left(\mathrm{n}\right)\right)\right.}\:=\:\mathrm{10} \\ $$$$\Rightarrow\frac{\emptyset\left(\mathrm{m}\right)\emptyset\left(\mathrm{n}\right)}{\mathrm{gcd}\left(\left(\emptyset\left(\mathrm{m}\right),\emptyset\left(\mathrm{n}\right)\right)\right.}\:=\:\mathrm{10} \\ $$$$\Rightarrow\mathrm{lcm}\left(\left(\emptyset\left(\mathrm{m}\right),\emptyset\left(\mathrm{n}\right)\right)=\mathrm{10}\right. \\ $$$$\mathrm{then}\:\emptyset\left(\mathrm{m}\right),\emptyset\left(\mathrm{n}\right)=\:\left(\mathrm{1},\mathrm{10}\right),\left(\mathrm{2},\mathrm{5}\right),\left(\mathrm{5},\mathrm{2}\right),\left(\mathrm{10},\mathrm{1}\right) \\ $$$$\mathrm{continue}.... \\ $$
Commented by Ajao yinka last updated on 26/Sep/19
$${complete}\:{it} \\ $$