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Find-LCD-2-100-1-2-120-1-




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

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