# [SOLVED]412.0.2 LCD and GCD

#### karush

##### Well-known member
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

Last edited:

#### skeeter

##### Well-known member
MHB Math Helper
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
well that makes a lot more sense

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

Last edited: