Chapter SH, Problem 11.6.22EP

To determine

The least common multiple of the given polynomials.

Answer to Problem 11.6.22EP

  $108a^2{b}^{2}c$

Explanation of Solution

Given:

The given polynomials are:

  $27a^{2}bc,36a{b}^2{c}^2$

Calculation:

The LCM is the smallest common multiple of all the terms given. The given terms can be factorized as:

  $\begin{array}{l}27a^{2}bc=3\cdot 3\cdot 3\cdot a\cdot a\cdot b\cdot c\\ 36a{b}^2{c}^2=2\cdot 2\cdot 3\cdot 3\cdot a\cdot b\cdot b\cdot c\end{array}$

The LCM can be calculated as:

  $\begin{array}{l}LCM=2\cdot 2\cdot 3\cdot 3\cdot 3\cdot a\cdot a\cdot b\cdot b\cdot c\\ LCM=108a^2{b}^{2}c\end{array}$