Chapter 4.4, Problem 16WE

(a).

To determine

To find: the GCF of the given monomials.

Answer to Problem 16WE

The GCF of $30,35,36,$ and $42$ is $1$

Explanation of Solution

Given information :

The given monomials:

  $30,35,36,42$

Calculation :

As per problem,

The prime factorization of the given monomials are:

  $\begin{array}{l}30=2\cdot 3\cdot 5\text{}\text{}\text{}\\ 35=5\cdot 7\\ 36=2^2\cdot 3^2\\ 42=2\cdot 3\cdot 7\end{array}$

To find GCF, take the least power of each common prime factor.

The given integers have no common factor except for $1$

Therefore, the GCF of $30,35,36,$ and $42$ is $1$

(b).

To determine

The LCM of the given monomials.

Answer to Problem 16WE

The LCM of $30,35,36,$ and $42$ is $1260$

Explanation of Solution

Given information :

The given monomials:

  $30,35,36,42$

Calculation :

As per problem,

The prime factorization of the given monomials are:

  $\begin{array}{l}30=2\cdot 3\cdot 5\text{}\text{}\text{}\\ 35=5\cdot 7\\ 36=2^2\cdot 3^2\\ 42=2\cdot 3\cdot 7\end{array}$

To find LCM, take the greatest power of each prime factor.

  $\text{LCM}=2^2\cdot 3^2\cdot 5\cdot 7=1260$

Therefore, the LCM of $30,35,36,$ and $42$ is $1260$