Chapter 4.4, Problem 18OE

To determine

To find : the GCF and LCM of the given monomials.

Answer to Problem 18OE

For the given monomials, the GCF is $x^2$ and LCM is $2x^{3}y$ .

Explanation of Solution

Given information :

The given monomials:

  $2x^3\text{ and }{x}^{2}y$

Calculation :

As per problem,

The coefficient of the monomial $2x^3$ is $2$ , which is a prime number.

The coefficient of the monomial $x^{2}y$ is $1$ .

To find GCF:

The GCF of $2$ and $1$ is $1$ .

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

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

  $\text{GCF}=1\cdot x^2=x^2$

To find LCM:

The LCM of $2$ and $1$ is $2$ .

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 $y$ .

  $\text{LCM}=2\cdot x^3\cdot y=2x^{3}y$

Therefore, for the given monomials, the GCF is $x^2$ and LCM is $2x^{3}y$ .