Find the least common denominator

The least common denominator is the least positive common multiple of two or more fraction denominators, providing the smallest shared unit size for expressing the fractions as equivalent fractions. Understanding that each numerator must be scaled by the same factor as its denominator—and that multiplying denominators is not always least—supports accurate fraction addition and subtraction; this scope concerns numerical fractions with positive whole-number denominators, not algebraic rational expressions or more advanced generalizations.

Detailed Explanation: Find the least common denominator

The least common denominator (LCD) is the smallest positive number that both denominators divide evenly into.

Example: Find the LCD of $\frac{5}{6}$ and $\frac{3}{8}$

List multiples of each denominator.

Multiples of $6$ :

6,\ 12,\ 18,\ 24,\ 30,\ldots

Multiples of $8$ :

8,\ 16,\ 24,\ 32,\ldots

Find the smallest number in both lists.

The first common multiple is $24$ , so:

\boxed{\text{LCD}=24}

Check the scaling factors.

To change $6$ to $24$ , multiply by $4$ :

6\times 4=24

To change $8$ to $24$ , multiply by $3$ :

8\times 3=24

When making equivalent fractions, multiply each numerator by the same factor:

\frac{5}{6}=\frac{5\times4}{6\times4}=\frac{20}{24}

\frac{3}{8}=\frac{3\times3}{8\times3}=\frac{9}{24}

The fractions now have the common denominator $24$ .

Remember: The LCD is the smallest common multiple, so multiplying the denominators is not always necessary.

Learn by doing: Find the least common denominator

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Fraction Addition - Mixed (No Simplifying Answers) - Two Changed Denominators

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