What is the least common denominator of 6 and 10?
Understand the Problem
The question is asking for the least common denominator (LCD) of the numbers 6 and 10. The LCD is the smallest number that both denominators can divide into without leaving a remainder. To find it, we can identify the multiples of each number and determine the smallest shared multiple.
Answer
$30$
Answer for screen readers
The least common denominator (LCD) of 6 and 10 is $30$.
Steps to Solve
- List the multiples of each number
Start by listing the first few multiples of 6 and 10.
Multiples of 6:
- 6, 12, 18, 24, 30, 36, ...
Multiples of 10:
- 10, 20, 30, 40, 50, ...
- Identify the common multiples
Next, look for numbers that appear in both lists of multiples.
The common multiples we can see are:
- 30, ...
- Select the least common multiple
Among the common multiples identified, select the smallest one.
The smallest number from the common multiples is:
- 30
- Conclusion
Therefore, the least common denominator (LCD) of 6 and 10 is 30.
The least common denominator (LCD) of 6 and 10 is $30$.
More Information
The least common denominator is very useful when adding or subtracting fractions. By finding the LCD, you can convert each fraction to an equivalent fraction with the same denominator.
Tips
One common mistake is only looking at the first multiples, rather than ensuring you've found the least common multiple. To avoid this, always check the resulting common multiples and confirm which is the smallest.
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