MHB What is the GCD and LCM of 35280 and 4158?

[karush]

Determine
$gcd(2^4 \cdot 3^2 \cdot 5 \cdot 7^2, 2 \cdot 3^3 \cdot 7 \cdot 11)=\boxed{126}$
and
$lcd(2^3 \cdot 3^2 \cdot 5,2 \cdot 3^3 \cdot 7 \cdot 11)=\boxed{83160}$
the number in the box is what W$\vert$A returned
ok i was doing stuff like this about a year ago but forgot
so assume to start
$gcd(35280,4158)$
but can't we take advantage of the powers

 

[skeeter]

prime factorization …

$35280 = 2^4 \cdot 3^2 \cdot 5 \cdot 7^2$
$4158 = 2 \cdot 3^3 \cdot 7 \cdot 11$

greatest common divisor includes the least power of all common factors …
$2 \cdot 3^2 \cdot 7 = 126$

least common multiple includes the greatest power of all common factors and the factors the two values do not have in common …
$2^4 \cdot 3^3 \cdot 5 \cdot 7^2 \cdot 11 = 1164240$

 

[karush]

Mahalo
so its just choosing the powers then calculate

 

[HallsofIvy]

Mahalo
so its just choosing the powers then calculate

Well, it is knowing what these things are, what their definitions are!

And note that it is "least common multiple", "lcm", NOT "lcd".

 

[karush]

corrected