Chapter 4.4, Problem 17OE

To determine

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

Answer to Problem 17OE

For the given monomials, the GCF is $ab$ and LCM is $a^2{b}^2$ .

Explanation of Solution

Given information :

The given monomials:

  $a^{2}b\text{ and }a{b}^2$

Calculation :

As per problem,

The coefficient of both the monomials is $1$ .

To find GCF, compare the powers of each variable occurring in both monomials. Use the power with the least exponent.

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

Compare $b$ and $b^2$ . Use $b$ .

  $\text{GCF}=ab$

To find LCM, compare the powers of each variable occurring in either monomial. Use the power with the greatest exponent.

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

Compare $b$ and $b^2$ . Use $b^2$ .

  $\text{LCM}=a^2\cdot b^2=a^2{b}^2$

Therefore, for the given monomials, the GCF is $ab$ and LCM is $a^2{b}^2$ .