Chapter 4.4, Problem 18WE

(a).

To determine

To find: the GCF of the given monomials.

Answer to Problem 18WE

The GCF of $49x^3$ and $35x^{2}y$ is $7x^2$ .

Explanation of Solution

Given information :

The given monomials:

  $49x^3,\text{}35x^{2}y$

Calculation :

The prime factorization of the coefficients are:

  $\begin{array}{l}49=7^2\\ 35=5\cdot 7\end{array}$

The GCF of $49$ and $35$ is $7$

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

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

  $\text{GCF}=7\cdot x^2=7x^2$

Therefore, the GCF of $49x^3$ and $35x^{2}y$ is $7x^2$ .

(b).

To determine

The LCM of the given monomials.

Answer to Problem 18WE

The LCM of $49x^3$ and $35x^{2}y$ is $245x^{3}y$ .

Explanation of Solution

Given information :

The given monomials:

  $49x^3,\text{}35x^{2}y$

Calculation :

As per problem,

The prime factorization of the coefficients are:

  $\begin{array}{l}49=7^2\\ 35=5\cdot 7\end{array}$

The LCM of $49$ and $35$ is

  $5\cdot 7^2=245$

Compare the powers of each variable occurring in either monomial. Use the power with the greatest exponent.

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

Use $y$ .

  $\text{LCM}=245\cdot x^3\cdot y=245x^{3}y$

Therefore, the LCM of $49x^3$ and $35x^{2}y$ is $245x^{3}y$ .