common denominator for 7 and 9
Understand the Problem
The question is asking for the least common denominator of the numbers 7 and 9, which is the smallest multiple that both numbers share. To find this, we typically look for the least common multiple (LCM) of the two numbers.
Answer
$63$
Answer for screen readers
The least common denominator (LCM) of 7 and 9 is $63$.
Steps to Solve
-
Identify the multiples of each number
First, we need to find the multiples of both numbers, 7 and 9.
Multiples of 7: $7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, \ldots$
Multiples of 9: $9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, \ldots$
-
Find the common multiples
Now we look for the numbers that appear in both lists of multiples.
Common multiples of 7 and 9: $63, 126, 189, \ldots$
-
Identify the least common multiple (LCM)
The least common multiple is the smallest number that is a common multiple of both numbers.
From our list, the smallest common multiple is $63$.
The least common denominator (LCM) of 7 and 9 is $63$.
More Information
The least common multiple can be useful in various mathematical applications, especially when adding or subtracting fractions. Understanding how to find the LCM helps in simplifying those processes.
Tips
- Forgetting to list enough multiples or listing them incorrectly. To avoid mistakes, be sure to check the lists you create and ensure they are correct.
- Confusing least common multiple (LCM) with greatest common divisor (GCD). It's important to remember that LCM deals with common multiples while GCD deals with common factors.
