Chapter 4.5, Problem 74E

To determine

To find the lowest common multipleof $6x^2,12x{y}^3$ .

Answer to Problem 74E

  $12x^2{y}^3$

Explanation of Solution

Given information: $6x^2,12x{y}^3$

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, to calculate the lowest common multiple for numbers and variables separately, post which multiplyboth.

Calculation:

Given, $6x^2,12x{y}^3$

First, find the greatest common factors of 6 and 12.

Prime Factors of $6=1\times 2\times 3$

Prime Factors of $12=1\times 2\times 2\times 3$

Lowest common multiple of 6 and 12 $=12$

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

Factors of $x^2=x\times x$

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

  $x\times x\times y\times y\times y$

  $=x^2{y}^3$

  $=12x^2{y}^3$ This is the lowest common multiple.