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[SOLVED] 412.0.2 LCD and GCD

karush

Well-known member
Jan 31, 2012
3,066
Determine
$\textit{gcd}(2^4 \cdot 3^2 \cdot 5 \cdot 7^2,\quad 2 \cdot 3^3 \cdot 7 \cdot 11)$
and
$\textit{lcm}(2^3 \cdot 3^2 \cdot 5,\quad 2 \cdot 3^3 \cdot 7 \cdot 11)$

ok the example appeared to have combine the 2 sets on gcd but I am still ???

there is no book answer for this:confused:
 
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skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
1,005
Greatest Common divisor ... think about how you would factor out the common terms from both prime decompositions if they were added

$(2^4 \cdot 3^2 \cdot 5 \cdot 7^2) + (2 \cdot 3^3 \cdot 7 \cdot 11)$

${\color{red}(2 \cdot 3^2 \cdot 7)} \bigg[(2^3 \cdot 5 \cdot 7)+ ( 3 \cdot 11) \bigg]$


Least Common Multiple ... think about obtaining a common denominator if both prime factor decompositions were denominators of two fractions

$\dfrac{x}{2^3 \cdot 3^2 \cdot 5} + \dfrac{y}{2 \cdot 3^3 \cdot 7 \cdot 11}$

$\dfrac{x(3 \cdot 7 \cdot 11) + y(2^2 \cdot 5)}{\color{red} 2^3 \cdot 3^3 \cdot 5 \cdot 7 \cdot 11}$
 

karush

Well-known member
Jan 31, 2012
3,066
well that makes a lot more sense

i don't think there is any need to multiple these out:cool:
 
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