Chapter 4.4, Problem 28WE

To determine

To find: the othermonomial.

Answer to Problem 28WE

The other monomial is $18x{y}^4$ .

Explanation of Solution

Given information:

The GCF of $12x^2{y}^3$ and another monomialis $6x{y}^3$ , and their LCM is $36x^2{y}^4$

Calculation:

As per problem,

Compare the coefficients,

The GCF of $12$ and the other numberis $6$ , so the number is a multiple of $6$

Their LCM is $36$ , so the numberis factor of $36$

The multiples of $6$ which are also factors of $36$ are

  $6,\text{ 12, 18 and 36}$

Now, LCM and GCF of $12$ and $6$ is $6$ , so the number is not $6$

And, the LCM and GCF of $12$ and $12$ is $12$ , so the number is not $12$

However, LCM and GCF of $12$ and $18$ is

  $\begin{array}{l}12=2\cdot 6\\ 18=3\cdot 6\\ \text{LCM=}2\cdot 3\cdot 6=36\end{array}$

Therefore, the coefficient of the monomial is $18$ .

The first monomial has $x^2$ as variable, and the GCF has x, so the other monomial has x.

The first monomial has $y^3$ as variable, but the LCM has $y^4$ , so the other monomial has $y^4$ .

Hence, the other monomial is $18x{y}^4$ .