Lowest Common Denominator
Short Course
This is a short course (slide show) in the basic concepts of calculating the lowest common denominator.
Finding the Lowest Common Denominator
You may have heard people say you need to compare apples to apples. You can’t compare apples to oranges. They mean that you can’t accurately compare things that aren’t the same. This is true with fractions. After you have simplified each fraction, the next step in adding or subtracting fractions is to convert them to the same denominator (apples to apples). Since most of the time whenever we add or subtract fractions they have different denominators. But how do we find this number?
There are a few ways to do this. Rather than discuss all of these techniques (some of them can be confusing), we will use a technique that straightforward and easy to understand:
Start with the larger denominator. Multiply it by 2. Then divide the smaller denominator into this number. Does it divide evenly (no remainder)? If so, this new number is the lowest common denominator.
If it doesn’t divide evenly, then multiply the larger denominator by 3. Again, divide the smaller denominator into this number. Does it divide evenly (with no remainder)? If so, this number is the lowest common denominator.
If it doesn’t divide evenly, repeat the steps multiplying by 4, 5, … until you find the number that is evenly divisible by both denominators. The largest common denominator is the product of both denominators. If both denominators are prime numbers, then the only common denominator will be the product of the two numbers.
Let’s look at some examples of this technique.
Examples
Now, let’s look at some more examples of this process. In these examples, the multiplicand will have many digits, but the multiplier will always be a single digit. Click on the link to show the steps to calculate the answer.
Example: Find LCD for 1/7 and 1/3
Example: Find LCD for 7/10 and 1/5
Example: Find LCD for 2/5 and 4/9
Example: Find LCD for 1/2 and 3/4
Example: Find LCD for 5/6 and 7/15