Find the least common denominator (LCD) of 9/7 and 5/6.
Understand the Problem
The question is asking to find the least common denominator (LCD) of the fractions 9/7 and 5/6. Finding the LCD involves determining the smallest multiple that both denominators can divide into without leaving a remainder.
Answer
The LCD of $\frac{9}{7}$ and $\frac{5}{6}$ is $42$.
Answer for screen readers
The least common denominator (LCD) is $42$.
Steps to Solve
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Identify the denominators The denominators of the fractions are $7$ and $6$.
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List the multiples of each denominator
- Multiples of $7$: $7, 14, 21, 28, 35, 42, \ldots$
- Multiples of $6$: $6, 12, 18, 24, 30, 36, 42, \ldots$
- Find the least common multiple (LCM) Identify the smallest multiple that appears in both lists:
- The common multiples: $42, \ldots$
- The least common multiple (LCM) is $42$.
- Conclusion The least common denominator (LCD) of the fractions $\frac{9}{7}$ and $\frac{5}{6}$ is $42$.
The least common denominator (LCD) is $42$.
More Information
The least common denominator (LCD) is useful when adding or subtracting fractions, as it allows fractions to be expressed with the same denominator. In this case, $42$ is the smallest multiple that both denominators divide evenly.
Tips
- Confusing LCM with GCD: Some may confuse least common multiple (LCM) with greatest common divisor (GCD). Remember, the LCD refers to LCM for denominators.
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