HOW DO I FIND THE LEAST COMMON DENOMINATOR
Method 1
Simply list the multiples of each number (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list.
Example: Find the least common multiple for 5, 6, and 15.
First we list the multiples of each number.
Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,...
Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,...
Multiples of 15 are 30, 45, 60, 75, 90,....
Now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list.
Therefore, the least common multiple of 5, 6 and 15 is 30.
To find the least common denominator (LCD), you need to follow these steps:
1. Identify the denominators: Take a look at the fractions you are working with and identify their denominators.
2. List the multiples: Write down the multiples of each denominator. Keep listing the multiples until you find a common multiple for all denominators.
3. Find the least common multiple (LCM): Determine the smallest number that appears in the list of multiples for all denominators. This is the least common multiple (LCM).
4. Use the LCM as the LCD: The LCM is also the least common denominator (LCD) for the fractions you are dealing with.
Let's go through an example to illustrate the process:
Example: Find the LCD for the fractions 3/4, 2/5, and 1/6.
1. Identify the denominators: The denominators in this case are 4, 5, and 6.
2. List the multiples:
- Multiples of 4: 4, 8, 12, 16, 20, 24, ...
- Multiples of 5: 5, 10, 15, 20, 25, 30, ...
- Multiples of 6: 6, 12, 18, 24, 30, 36, ...
3. Find the least common multiple (LCM): The LCM of 4, 5, and 6 is 60 since it is the smallest number that appears in the list of multiples for all denominators.
4. Use the LCM as the LCD: The LCD for 3/4, 2/5, and 1/6 is 60.
Therefore, the LCD is 60 in this example.