# What is the GCF and LCM for 52r2s, 78rs^2t?

Oct 9, 2015

First factorize:
$52 {r}^{2} s = 2 \cdot 2 \cdot 13 \cdot r \cdot r \cdot s$ and
$78 r {s}^{2} t = 2 \cdot 3 \cdot 13 \cdot r \cdot s \cdot s \cdot t$

#### Explanation:

GCF :
Take all the common factors:
$2 \cdot 13 \cdot r \cdot s = 26 r s$

Check :
$\frac{52 {r}^{2} s}{26 r s} = 2 r$ and $\frac{78 r {s}^{2} t}{26 r s} = 3 s t$ have no common factors

LCM :
Take all the factors to their highest degree:
$2 \cdot 2 \cdot 3 \cdot 13 \cdot r \cdot r \cdot s \cdot s \cdot t = 156 {r}^{2} {s}^{2} t$

Check :
$\frac{156 {r}^{2} {s}^{2} t}{52 {r}^{2} s} = 3 s t$ and $\frac{156 {r}^{2} {s}^{2} t}{78 r {s}^{2} t} = 2 r$