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Here are a few recommended readings before getting started with this lesson.
Background to Help Understand Numbers
Background to Help Understand Multiples
A common denominator is a denominator that is shared between two or more fractions. Consider a few examples.
Pair of Fractions  Common Denominator 

$32 $ and $35 $  $3$ 
$108 $ and $105 $  $10$ 
$1711 $ and $176 $  $17$ 
There are a lot of possible common denominators that fractions can have. However, it is almost always easier to deal with smaller numbers. This is when the least common denominator comes in handy!
The least common denominator (LCD) of two fractions is the least common multiple (LCM) of the denominators of the fractions. In other words, the least common denominator is the smallest of all the common denominators. Some examples are provided in the table below.
Fractions  Denominators  Multiples of Denominators  Common Denominators  LCM of Denominators (LCD) 

$32 $ and $21 $  $3$ and $2$  $Multiples of3:Multiples of2: 3,6,9,12,15,…2,4,6,8,10,12,… $

$6,$ $12$  $6$ 
$65 $ and $41 $  $6$ and $4$  $Multiples of6:Multiples of4: 6,12,18,24,30,…4,8,12,16,20,24,… $

$12,$ $24$  $12$ 
$41 $ and $25 $  $4$ and $2$  $Multiples of4:Multiples of2: 4,8,12,…2,4,6,8,10,12,… $

$4,$ $8,$ $12$  $4$ 
The least common denominator is used when adding or subtracting fractions with different denominators.
To sum up, finding the least common denominator is the same as finding the least common multiple of the denominators. When fractions have a common denominator, which is most often the LCD, they are ready to be compared by comparing their numerators.
Fractions  $114 $ and $119 $ 

Numerators  $4<9$ 
Conclusion  $114 <119 $ 
Same Denominator  Same Numerator 

The greater numerator, the greater the fraction.  The smaller denominator, the greater the fraction. 
Notice that the $7$ pieces of the first fraction are much larger than the $16$ pieces of the second. The numerator of each fraction indicates how many pieces get picked. Since the numerators are the same, $5$ pieces are selected from each whole. Which fraction has a larger selected section?
The total selected area is greater in the first fraction than in the second because each of the pieces is bigger. This is why the fraction with the smaller denominator is greater if the numerators are the same.
Consider the given pair of fractions. Which one is greater? Choose the correct sign to complete the expression. If necessary, rewrite the fractions such that they have a common denominator.
Rewrite the fractions so that they have a common denominator. Find it by determining the LCM of the denominators.
Denominator  Calculating the Quotient  Factor 

$6$  $660 $  $10$ 
$20$  $2060 $  $3$ 
$3$  $360 $  $20$ 
$5$  $560 $  $12$ 
Fraction  Equivalent Fraction 

$65 $  $6050 $ 
$205 $  $6015 $ 
$32 $  $6040 $ 
$51 $  $6012 $ 
Tiffaniqua, LaShay, Kevin, and one of their classmates are working on a biology project comparing four different flowers. Each of them was assigned a specific flower. After some research time, they met up to discuss what they found out.
For their project, they need to compare various data points. However, they discovered that they had collected some of these values in different forms and they could not compare the values. Help the students by ordering the numbers from least to greatest.Rewrite the numbers so that they are in the same form. Then, plot the numbers on a number line to help place them in order.
Multiply by $100$
$ca ⋅b=ca⋅b $
Multiply