Vocabulary

Rational Number – a number that can be expressed as a ratio of two integers written as a fraction, in which the denominator is not zero.

Common Denominator – a common multiple of the denominators of two or more fractions.

Lowest Common Denominator (LCD) -   the least common multiple (LCM) of the denominators. 

Greatest Common Factor (GCF) – the largest number (factor) that goes into the denominators.

Concepts

Find the LCD of two or more fractions.

Rules

1. To find the LCD, list the prime factors of each number.  
2.  Look for the most occurrence of each of those prime factors.
3. Find the products of these factors.
The answer is the LCD.

Example

Choose the LCD for the numbers below.

$\mathrm{-}\frac{5}{12}\mathrm{ , }\frac{3}{8}\mathrm{ , }\frac{5}{6}$

Solution

1. Find the LCM.
A. List the prime factors for each denominator.
12 = 2 × 2 × 3
8 = 2 × 2 × 2
6 = 2 × 3

B. Multiply each factor the greatest number of times it occurs in either number. 
2 occurs three times in 8. 3 occurs only once in 12 and 6.

2. LCD = (2 × 2 × 2) × (3) = 24
Answer: 24

Pre-requisite Skills

Fractions – Greatest Common Factor (GCF) (6.4.1)

Fractions – Least Common Multiple (LCM) (6.4.2)