Mathematics
Grade 8
15 min
Least common denominator
Least common denominator
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define multiples, common multiples, and the Least Common Multiple (LCM).
Find the Least Common Multiple (LCM) of two or more whole numbers using various methods.
Identify the Least Common Denominator (LCD) of two or more rational numbers.
Convert rational numbers into equivalent fractions using the LCD.
Use the LCD to compare and order rational numbers.
Apply the LCD as a foundational step for adding and subtracting rational numbers.
Ever tried to combine ingredients for a recipe but the measurements were in different units? 🍰 Or maybe you've tried to compare two different sized pieces of pizza? 🍕 Understanding the Least Common Denominator helps us make sense of these situations!
In this lesson, you'll learn what the Least Common Denominator...
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Key Concepts & Vocabulary
TermDefinitionExample
MultipleA multiple of a number is the result of multiplying that number by an integer (e.g., multiples of 3 are 3, 6, 9, 12...).Multiples of 4 are: 4, 8, 12, 16, 20, 24, ...
Common MultipleA common multiple of two or more numbers is a number that is a multiple of all of them.For 4 and 6, common multiples include 12, 24, 36, ...
Least Common Multiple (LCM)The smallest positive common multiple of two or more numbers. It's the smallest number that is a multiple of all the given numbers.The LCM of 4 and 6 is 12.
DenominatorThe bottom number in a fraction, representing the total number of equal parts into which the whole is divided.In the fraction $\frac{3}{4}$, the denominator is 4.
Least Common Denominator (LCD)The Least Common Multiple (LCM) of the denominators of...
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Core Formulas
Finding LCM by Listing Multiples
List the multiples of each number until you find the smallest positive multiple that appears in all lists.
This method is effective for smaller numbers. Write out the multiples for each denominator and identify the first number they share.
Finding LCM by Prime Factorization
1. Find the prime factorization of each number. 2. For each prime factor, take the highest power that appears in any of the factorizations. 3. Multiply these highest powers together to get the LCM.
This method is generally more efficient for larger numbers. It ensures you capture all necessary prime factors to form the smallest common multiple.
Determining the LCD
The Least Common Denominator (LCD) of a set of fractions is the Least Common Multiple (LCM) of their den...
5 more steps in this tutorial
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Challenging
What is the sum of the numerators of 3/8, 1/12, and 5/16 after converting them to equivalent fractions using their LCD?
A.9
B.29
C.37
D.48
Challenging
A student converted 5/12 and 7/18 to 15/36 and 14/36 to compare them. Was 36 the Least Common Denominator? How do you know?
A.Yes, because 36 is a multiple of both 12 and 18.
B.Yes, because the prime factorization of 12 (2²×3) and 18 (2×3²) results in an LCM of 2²×3² = 36.
C.No, the LCD is 72 because 12 x 6 = 72 and 18 x 4 = 72.
D.No, the LCD is 216 because 12 x 18 = 216.
Challenging
What is the LCD for three fractions with denominators whose prime factorizations are 2³×5, 2²×3×5, and 3²×5²?
A.2² × 3 × 5
B.2⁵ × 3³ × 5⁴
C.2³ × 3² × 5
D.2³ × 3² × 5²
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