The LCD in mathematics stands for `least common denominator`. The LCD indicates the smallest common denominator bottom of a [[fractions|fraction]]. The LCD is crucial for adding or subtracting fractions! The LCD is the smallest number that two or more denominators can evenly divide into. Example: > [!NOTE] > Problem: $\frac{1}{3} + \frac{2}{9}$ > LCD: > - $3 = 3$ - prime factors of 3 > - $9 = 3^2$ - prime factors of 9 > LCD = $3^2$ > ANSWER: $\frac{1\cdot3}{3\cdot3} + \frac{2}{9} = \frac{5}{9}$ Sure! Here's an updated version of your "Calculate LCD" section with a clear example added: --- ## Calculate LCD Calculating the LCD is super simple. You start by calculating the [[prime factors]] for each of your denominators. Once that is done, combine all the unique prime factors by only taking the **highest power** of each prime factor. The product of all those values you just calculated is the LCD. **Example:** > [!TIP] > Find the LCD of $\frac{1}{6}$ and $\frac{1}{8}$ > > - $6 = 2 \cdot 3$ > > - $8 = 2^3$ > > > Take the **highest powers** of each prime: > > - $2^3$ (from 8) > > - $3$ (from 6) > > > LCD = $2^3 \cdot 3 = 8 \cdot 3 = 24$ > > So, $\frac{1}{6} = \frac{4}{24}$ and $\frac{1}{8} = \frac{3}{24}$ ## Nuances / Tips - The LCD is just he [[lcm]] of the denominators. - You only need the lcm for fraction addition and subtraction - On smaller denominators the LCD can be found with mental math - In fractions with variables, expressions can be the LCD $\frac{1}{x+1}$ and $\frac{1}{x^2-1}$ ## Practice Tests - [[common denominator practice packet.pdf]]