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K.4 Least common denominator

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What is the Least Common Denominator?

The Least Common Denominator (LCD) is the smallest denominator that two or more fractions share when they are written with equivalent denominators. It allows you to compare, add, or subtract fractions easily.

Example:
  • 12 and 13 have denominators 2 and 3.
  • The least common denominator of 2 and 3 is 6.
  • So, 12 = 36 and 13 = 26.
Note

The LCD is found by finding the least common multiple (LCM) of the denominators.

How to find the Least Common Denominator

To find the LCD, list the multiples of each denominator until you find the smallest one that they have in common.

Steps:
  • Find the denominators: 4 and 6.
  • List multiples of 4: 4, 8, 12, 16, 20, ...
  • List multiples of 6: 6, 12, 18, 24, ...
  • The smallest common multiple is 12.
  • So, the LCD of 4 and 6 is 12.
Note

It can help to know your multiplication facts well—this makes finding the LCD much faster.

Using the LCD to add or subtract fractions

Before adding or subtracting fractions, you must make sure the denominators are the same. Use the LCD to rewrite the fractions with equivalent denominators.

Example:
  • Add 13 + 14.
  • The LCD of 3 and 4 is 12.
  • Convert: 13 = 412 and 14 = 312.
  • Add the numerators: 4 + 3 = 7.
  • The sum is 712.
Note

The denominator does not change when adding or subtracting fractions—it stays the same after you find the LCD.

Tips for finding the LCD quickly

Sometimes you can find the LCD by using simple patterns or multiplication facts instead of listing all multiples.

Examples:
  • If one denominator is a multiple of the other, the larger one is the LCD.
    Example: For 5 and 10, the LCD is 10.
  • For denominators like 8 and 12, you can divide their product by their greatest common factor (GCF):
    8 × 12 = 96; GCF = 4 → 96 ÷ 4 = 24, so LCD = 24.
Note

Understanding both the greatest common factor (GCF) and the least common multiple (LCM) helps you find the LCD faster and check your work.