Chapter 4.4, Problem 20OE

To determine

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

Answer to Problem 20OE

For the given monomials, the GCF is $2u{v}^2$ and LCM is $4u^2{v}^{2}w$ .

Explanation of Solution

Given information :

The given monomials:

  $4u{v}^{2}w\text{ and }-2u^2{v}^2$

Calculation :

As per problem,

The prime factorization of the coefficients are:

  $4=2^2$

  $2$ is a prime number.

1. To find GCF:

The GCF of $4$ and $-2$ is $2$ .

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

Compare $u$ and $u^2$ . Use $u$ .

Use $v^2$ .

$\text{GCF}=2\cdot u\cdot v^2=2u{v}^2$

2. To find LCM:

The LCM of $4$ and $-2$ is

$2^2=4$

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

Compare $u$ and $u^2$ . Use $u^2$ .

Use $v^2$ .Use $w$ .

  $\text{LCM}=4\cdot u^2\cdot v^2\cdot w=4u^2{v}^{2}w$

Therefore, for the given monomials, the GCF is $2u{v}^2$ and LCM is $4u^2{v}^{2}w$ .