Chapter 4.5, Problem 76E

To determine

To find the lowest common multiple of $4x^3,7x{y}^2$ .

Answer to Problem 76E

  $28x^3{y}^2$

Explanation of Solution

Given information: $4x^3,7x{y}^2$

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 multiplyboth.

Calculation:

Given, $4x^3,7x{y}^2$

Since 4 and 7 are co-prime, the lowest common multiple here would be

  $=4\times 7$

  $=28$

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

Factors of $x^3=x\times x\times x$

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

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

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

  $=x^3{y}^2$

  $=28x^3{y}^2$ This is the lowest common multiple.