Chapter 8.2, Problem 18PPS

To determine

To find: the LCM of polynomials.

Answer to Problem 18PPS

The LCM of the polynomials is $120a^{2}bc{d}^4$ .

Explanation of Solution

Given information:

The polynomials are $24cd,40a^2{c}^3{d}^4,15ab{d}^3$

Calculation: to find the LCM od the polynomials, first factorise the polynomials and then multiply one of each factor and repeat factors with highest exponents,

  $\begin{array}{l}24cd=2·2·2·3·c·d\text{ [factor]}\\ 40a^2{c}^3{d}^4=2·2·2·5·a·a·c·c·c·d·d·d·d\text{ [factor]}\\ 15ab{d}^3=5·3·a·b·d^3\text{ [factor]}\\ \text{LCM}=2·2·2·3·5·a^{2}b{c}^3{d}^4\text{ [multiply the common factor and each factors]}\\ \text{LCM}=120a^{2}bc{d}^4\end{array}$

Thus, the LCM of the polynomials is $120a^{2}bc{d}^4$ .