Chapter 12, Problem 50CUR

To determine

To find: The greatest common factor and least common multiple of $7x^2{y}^3,5x^3{y}^4$ .

Answer to Problem 50CUR

The Greatest Common Factor $=x^2{y}^3$ and Least Common Multiple $=35x^3{y}^4$ .

Explanation of Solution

Given information : The monomials are $7x^2{y}^3$ and $5x^3{y}^4$ .

Concept used : The greatest number that is a factor of two (or more) other numbers. When we find all the factors of two or more numbers, and some factors are the same, then the largest of those common factors is greatest common factor.

The least common multiple of two numbers is the smallest number (not zero) that is a multiple of both.

Calculation :

Factors of $7x^2{y}^3=1\times 7\times x\times x\times y\times y\times y$

And factors of $5x^3{y}^4=1\times 5\times x\times x\times x\times y\times y\times y\times y$

So, Greatest Common Factor $=x^2{y}^3$ .

And Least Common Multiple $=35x^3{y}^4$ .

Thus, the Greatest Common Factor $=x^2{y}^3$ and Least Common Multiple $=35x^3{y}^4$ .