Question Number 211310 by hardmath last updated on 05/Sep/24
$$\mathrm{Find}: \\ $$$$\mathrm{LCD}\left(\mathrm{2}^{\mathrm{100}} \:−\:\mathrm{1}\:\:;\:\:\mathrm{2}^{\mathrm{120}} \:−\:\mathrm{1}\right)\:=\:? \\ $$
Answered by A5T last updated on 05/Sep/24
$${What}\:{is}\:{LCD}?\:{Do}\:{you}\:{mean}\:{GCD}\:{or}\:{LCM}? \\ $$$${GCD}×{LCM}=\left(\mathrm{2}^{\mathrm{100}} −\mathrm{1}\right)\left(\mathrm{2}^{\mathrm{120}} −\mathrm{1}\right) \\ $$$${GCD}=\mathrm{2}^{{gcd}\left(\mathrm{100},\mathrm{120}\right)} −\mathrm{1}=\mathrm{2}^{\mathrm{20}} −\mathrm{1} \\ $$$$\Rightarrow{LCM}=\frac{\left(\mathrm{2}^{\mathrm{100}} −\mathrm{1}\right)\left(\mathrm{2}^{\mathrm{120}} −\mathrm{1}\right)}{\mathrm{2}^{\mathrm{20}} −\mathrm{1}} \\ $$
Commented by hardmath last updated on 05/Sep/24
$$\mathrm{LCM}\:\mathrm{yes}\:\mathrm{sorry}\:\mathrm{dear}\:\mathrm{ser} \\ $$
Commented by hardmath last updated on 06/Sep/24
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{dear}\:\mathrm{ser}… \\ $$$$\mathrm{GCD}\:=\:? \\ $$
Commented by A5T last updated on 06/Sep/24
$${GCD}={greatest}\:{common}\:{divisor}=\mathrm{2}^{\mathrm{20}} −\mathrm{1} \\ $$