Chapter 4.6, Problem 4ST

a.

To determine

To find the Greatest common factor (GCF).

Answer to Problem 4ST

The greatest common factor is $6p^3{q}^{2}r,8p^2{q}^2{r}^2,4p^3{q}^3=2p^2{q}^2$

Explanation of Solution

Given: The integers is , $6p^3{q}^{2}r,8p^2{q}^2{r}^2,4p^3{q}^3$

Concept Used: Greatest common factor (GCF).

The Greatest common factor (GCF) of two or more integers is the greatest integer that is a factor of each.

Calculation: The Greatest common factor (GCF) is obtained as,

  $6p^3{q}^{2}r,8p^2{q}^2{r}^2,4p^3{q}^3$

The GCF of $6,8$ and $4$ is $2$ .

Compare the power of each variable occurring in both monominals. Use the power with the least exponent.

Compare $p^3,p^2$ and $p^3$ . Use $p^2$ .

Compare $q^2$ and $q^3$ . Use $q^2$ .

Hence, the greatest common factor is $6p^3{q}^{2}r,8p^2{q}^2{r}^2,4p^3{q}^3=2p^2{q}^2$ .

b.

To determine

To find the least common multiple (LCM).

Answer to Problem 4ST

The least common multiple $6p^3{q}^{2}r,8p^2{q}^2{r}^2,4p^3{q}^3=24p^3{q}^3{r}^2$ .

Explanation of Solution

Given: The integers is , $6p^3{q}^{2}r,8p^2{q}^2{r}^2,4p^3{q}^3$ .

Concept Used: Least common multiple (LCM) The least common multiple (LCM) of two or more integers is the least positive integer having each as a factor.

Calculation: The least common multiple (LCM) is obtained as,

  $6p^3{q}^{2}r,8p^2{q}^2{r}^2,4p^3{q}^3$

The LCM of $6,8$ and $4$ is $24$ .

Compare the power of each variable occurring in either monominal. Use the power with the greatest exponents.

Compare $p^3,p^2$ and $p^3$ . Use $p^3$ .

Compare $q^2$ and $q^3$ . Use $q^3$ .

Compare $r$ and $r^2$ . Use $r^2$ .

Hence, the least common multiple $6p^3{q}^{2}r,8p^2{q}^2{r}^2,4p^3{q}^3=24p^3{q}^3{r}^2$ .