Chapter 4.5, Problem 77E

To determine

To find the lowest common multiple of $9x^2{y}^3,8xy$ .

Answer to Problem 77E

  $72x^2{y}^3$

Explanation of Solution

Given information: $9x^2{y}^3,8xy$

To find the lowest common multiple of 2 or more algebraic terms, find the product of the factors of the terms. This product shall comprise of the prime factors present in all the terms in such a way that the lowest common multiple shall be completely divisible by the terms.

For algebraic terms, calculate the lowest common multiple for numbers and variables separately, post which multiply both.

Calculation:

Given, $9x^2{y}^3,8xy$

Since 8 and 9 are co-prime, the lowest common multiple here would be

  $=8\times 9$

  $=72$

Hence the lowest common multiple of $x^2{y}^3\&xy$

Factors of $xy=x\times y$

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

Lowest common multiple of $x^2{y}^3\&xy$

  $=x\times x\times y\times y\times y$

  $=x^2{y}^3$

  $=72x^2{y}^3$ This is the lowest common multiple.