AlgebraStructure & Method · Book 1All Chapters

Adding and Subtracting Fractions

6-4Least Common Denominators

Overview

The LCD is the LCM of the denominators—the product of the highest power of each factor that appears.

Key ideas

  • Factor each denominator.
  • Take the highest power of every factor.
  • Multiply.

Worked examples

Example 1

Problem. LCD of 1/6 and 1/8.

Solution. LCM(6,8) = 24

Example 2

Problem. LCD of 1/x and 1/(x^2).

Solution. x^2

Practice

Try each one. Click Show answer when ready.

  1. 1.

    LCD of 1/4 and 1/6.

  2. 2.

    LCD of 1/(x) and 1/(x − 1).

  3. 3.

    LCD of 1/(2x) and 1/(3x^2).

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Find the LCD of 6x²y and 9xy³.

  2. 2.

    Find the LCD of x² − 4 and x + 2.