Question

How do you find the LCD of $x - 4$ and $x + 2$?

Answer 1

Hint: LCD: Lowest Common Denominator : Lowest common denominator can be found by multiplying the highest exponent prime factors of the denominator . For this we have to calculate the prime factor of $1$ and $1$ . The lowest common denominator is also known as Least common multiple and this can be calculated in two ways ; with the help of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Complete step by step solution:
Given $x - 4$ and $x + 2$
We can write this as , $\dfrac{{x - 4}}{1}$ and $\dfrac{{x + 2}}{1}$ ,
Now we know we have to do prime factorization of $1$ and $1$ .
Prime factorization: It’s the process where the original given number is expressed as the product of
prime numbers.
Factorization of $1$ :
$1 = 1$
Factorization of $1$ :
$1 = 1$
Lowest common divisor can be found by multiplying the highest exponent factors of the denominator that is $1$ and $1$ .
Therefore, we can write ,
LCM of $1$ and $1$ is given as ,
$ = 1$

Therefore, we can write that the LCM of $1$ and $1$ is $1$ .
And LCD of $x - 4$ and $x + 2$ is also $1$ .

Note: Questions similar in nature as that of above can be approached in a similar manner and we can solve it easily. The above question can also be done by simply listing all the possible factors of both the given numbers and then taking the greatest common factor by just comparing the list of factors to find the common factors and choosing the greatest factor among it then applying the formula that is LCM is equals to the product of the HCF and the product of the numbers.