Least common denominator

Definition

The least common denominator (LCD) is the smallest positive number that is a multiple of the denominators of two or more fractions. It is used to add, subtract, or compare fractions.

5 Must Know Facts For Your Next Test

1. To find the LCD, list the multiples of each denominator and identify the smallest common multiple.
2. The LCD is essential for performing operations with rational expressions involving different denominators.
3. When solving linear equations in one variable that involve fractions, converting all terms to have the LCD can simplify the process.
4. Finding the LCD helps avoid mistakes related to improper addition or subtraction of fractions.
5. The LCD is always greater than or equal to the largest denominator in the set.

Review Questions

• What steps are involved in finding the least common denominator between two fractions?
• How does using the least common denominator simplify adding and subtracting rational expressions?
• Why is it important to use the least common denominator when solving linear equations involving fractions?

Related terms

Greatest Common Divisor (GCD): The greatest common divisor (GCD) is the largest positive integer that divides two or more integers without leaving a remainder.

Rational Expression: A rational expression is a fraction where both the numerator and the denominator are polynomials.

Linear Equation: $A\ linear\ equation$ $is\ an\ algebraic\ equation\ in\ which\ each\ term\ has$ $an exponent$ $no$ $greater$ $than one,$ $and it forms a straight line when graphed.$