Mathematics
Grade 5
15 min
Least common denominator
Least common denominator
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define 'denominator', 'multiple', 'common multiple', and 'least common denominator'.
List multiples of two or more given numbers.
Identify the least common multiple (LCM) of two or more numbers.
Find the least common denominator (LCD) for a set of fractions.
Use the LCD to create equivalent fractions.
Explain why finding the LCD is important for comparing and adding fractions.
Have you ever tried to compare two slices of pizza that were cut into different numbers of pieces? 🍕 It can be tricky to tell which is bigger!
In this lesson, we'll learn about the Least Common Denominator (LCD). This special number helps us make fractions 'speak the same language' so we can easily compare them, put them in or...
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Key Concepts & Vocabulary
TermDefinitionExample
DenominatorThe bottom number in a fraction that tells us how many equal parts the whole is divided into.In the fraction $\frac{3}{4}$, the '4' is the denominator, meaning the whole is divided into 4 equal parts.
MultipleThe result of multiplying a number by another whole number (not zero). It's like counting by that number.Multiples of 3 are 3, 6, 9, 12, 15, ... (3x1, 3x2, 3x3, etc.)
Common MultipleA number that is a multiple of two or more different numbers.For 2 and 3, common multiples include 6, 12, 18, ... (6 is a multiple of 2 and 3, 12 is a multiple of 2 and 3).
Least Common Multiple (LCM)The smallest non-zero common multiple of two or more numbers.For 2 and 3, the multiples of 2 are {2, 4, 6, 8, 10, 12,...} and multiples of 3 are {3, 6, 9, 12,.....
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Core Formulas
Finding Multiples
To find multiples of a number 'n', multiply 'n' by 1, 2, 3, 4, and so on: $n \times 1, n \times 2, n \times 3, ...$
This rule helps you list out the multiples for each denominator, which is the first step to finding common multiples.
Identifying the Least Common Multiple (LCM)
List the multiples for each number. Find the smallest number that appears in all lists. This is the LCM.
The LCM of the denominators is exactly what we call the Least Common Denominator (LCD). This is the core step in finding the LCD.
Using LCD to Create Equivalent Fractions
To change a fraction $\frac{a}{b}$ to an equivalent fraction with a new denominator 'D' (where 'D' is the LCD), multiply both the numerator and the denominator by the...
5 more steps in this tutorial
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Challenging
What is the LCD for the fractions 1/3, 5/9, and 7/12?
A.36
B.108
C.24
D.9
Challenging
A student needs the LCD for 7/10 and 3/15. They list multiples of 10 (10, 20, 30...) and 15 (15, 30...). They also calculate 10 x 15 = 150. Which number should they use as the LCD and why?
A.150, because multiplying the denominators is the easiest method.
B.30, because it is the *least* common multiple, which makes the problem simpler.
C.150, because it is a bigger number and more likely to be correct.
D.30, because it is the only number that appears in both lists of multiples.
Challenging
If you find the LCD for two fractions, and the LCD is 30, which of these pairs could have been the original denominators?
A.5 and 6
B.2 and 15
C.10 and 3
D.All of the above
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