Least common denominator

Definition

The least common denominator (LCD) of two or more rational expressions is the smallest positive integer that is divisible by each of their denominators. It is essential for adding, subtracting, or comparing fractions.

5 Must Know Facts For Your Next Test

1. To find the LCD, identify the least common multiple (LCM) of the denominators.
2. The LCD provides a common base for combining rational expressions.
3. Factoring each denominator into its prime factors helps in determining the LCD.
4. Using the LCD simplifies the process of solving equations involving rational expressions.
5. The LCD is particularly useful when dealing with complex fractions.

Review Questions

• How do you determine the least common denominator between two rational expressions?
• Why is finding the least common denominator important when simplifying fractions?
• What steps are involved in finding the least common denominator when given multiple denominators?

Related terms

Least Common Multiple (LCM): The smallest positive integer that is divisible by each of two or more integers.

Rational Expression:

A fraction where both the numerator and the denominator are polynomials.

Prime Factorization: Breaking down a composite number into a product of its prime factors.