Question

What is the least common multiple of 62 +39 - 21 and 6x² +54x+84? O 6x² +54x+84 6x² +93x +63 62³ +52x² + 111x − 42 O 12x³ + 102x² + 114 - 84

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expressions

$6x^2+39x-21\text{ }and\text{ }6x^2+54x+84$

STEP 2: Define the least common multiple

The Least Common Multiple ( LCM ) is also referred to as the Lowest Common Multiple ( LCM ) and Least Common Divisor ( LCD) . For two integers a and b, denoted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b.

STEP 3: Find the LCM

Factorize the first expression

$6x^2+39x-21=3(2x-1)(x-7)$

Factorize the second expression:

$6x^2+54x+84=3(x+2)(x+7)$

Calculating the LCM, we have:

$\begin{gathered} \mathrm{Multiply\:each\:factor\:with\:the\:highest\:power:} \\ 2\cdot \left(2x-1\right)\cdot \:3\cdot \left(x+2\right)\cdot \left(x+7\right) \\ Simplify \\ 6\left(2x-1\right)\left(x+2\right)\left(x+7\right) \end{gathered}$

Evlauating the result gives:

$12x^3+102x^2+114x-84$

Hence, the LCM is:

$12x^3+102x^2+114x-84$