Chapter 4.6, Problem 3ST

a.

To determine

To find the Greatest common factor (GCF).

Answer to Problem 3ST

The greatest common factor is $36a^2{b}^3,54ab{c}^2=18ab$

Explanation of Solution

Given: The integers is , $36a^2{b}^3,54ab{c}^2$

Concept Used: Greatest common factor (GCF).

The Greatest common factor (GCF) of two or more integers is the greatest integer that is a factor of each.

Calculation: The Greatest common factor (GCF) is obtained as,

  $36a^2{b}^3,54ab{c}^2$

The GCF of $36$ and $54$ is $18$ .

Compare the power of each variable occurring in both monominals. Use the power with the least exponents.

Compare $a^2$ and $a$ . Use $a$ .

Compare $b^3$ and $b$ . Use $b$ .

Hence, the greatest common factor is $36a^2{b}^3,54ab{c}^2=18ab$

b.

To determine

To find the least common multiple (LCM).

Answer to Problem 3ST

The least common multiple $36a^2{b}^3,54ab{c}^2=108a^2{b}^3{c}^2$ .

Explanation of Solution

Given: The integers is , $36a^2{b}^3,54ab{c}^2$

Concept Used: Least common multiple (LCM) The least common multiple (LCM) of two or more integers is the least positive integer having each as a factor.

Calculation: The least common multiple (LCM) is obtained as,

  $36a^2{b}^3,54ab{c}^2$

The LCM of $36$ and $54$ is $108$ .

Compare the power of each variable occurring in either monominal. Use the power with the greatest exponents.

Compare $a^2$ and $a$ . Use $a^2$ .

Compare $b^3$ and $b$ . Use $b^3$ .

Use $c^2$ .

Hence, the least common multiple $36a^2{b}^3,54ab{c}^2=108a^2{b}^3{c}^2$ .