To add or subtract two fractions, they must have a common denominator.
How can we add two fractions with unlike denominators, like this?
1/3 + 1/9 = ?
We have to turn them into equivalent fractions with a common denominator.
First, we need to find a common denominator, which means a common multiple of both denominators.
We can list the multiples of each denominator by skip counting:
We can always multiply the denominators together, 3 × 9, to get a common denominator, 27, but it won't always be the least common denominator, 9.
The Least Common Denominator is short for the least common multiple of the denominators.
When you use the LCD instead of just any common denominator, it keeps your answer in its simplest terms.
Take a look at our answer if we use 27 as our common denominator:
Tip: 👆 here we turned each addend into an equivalent one with a common denominator of 27.
If instead we convert both addends to the LCD, 9, we get a simpler answer!
Both ways are correct, because 12/27 = 4/9, but using the LCD made the math a little easier.
There are a few ways to finding the LCD.
Let's learn one way, called "listing multiples", with an example.
Find the LCD of 1/3 and 1/5.
1️⃣ Start by finding the first multiple of the bigger denominator.
Tip: The first multiple is always the number itself. This is the product of the number multiplied by 1.
The bigger denominator is 5.
Its first multiple is 5.
2️⃣ Check if this number is a multiple of the smaller denominator.
If yes, then you've found the LCD.
If not, then you have to go on to the next step.
Let's try this with our example:
The smaller denominator is 3. Is 5 one of its multiples?
Let's list some multiples of 3:
3, 6, 9...
We're now at 9, but haven't listed 5 yet. So 5 is not a multiple of 3. It can't be the LCD. ✖️
Tip: We also can tell because 3 doesn't divide 5 evenly.
We need to keep going.
3️⃣ List the next multiple of the bigger denominator.
The next multiple for 5 is 10.
Is 10 a multiple of the smaller denominator?
We can list more multiples of 3.
3, 6, 9, 12...
10 is not a multiple of 3.
So, 10 is not the LCD. ✖️
Let's continue listing the multiples for 5, the larger denominator...
5, 10, 15...
Is 15 a multiple of 3?
Let's see...
3, 6, 9, 12, 15
15 is a multiple of 3! 👍
Tip: this is the same as saying 15 is divided evenly by 3.
So we've found the LCD for our fractions!
15 is the LCD for 1/3 and 1/5. ✅
Let's practice finding the LCD together one more time.
If we multiply 3 × 9, we get 27.
27 is a common denominator for 1/3 and 1/9. ✅
It's not the least common denominator, however.
Let's find the LCD together.
1️⃣ Find the first multiple of the bigger denominator.
The bigger denominator is 9.
Its first multiple is 9.
2️⃣ Ask, "Is 9 a multiple of 3?"
Yes, it is.
"Can we divide 9 by 3 without a remainder?"
Yes, we can. 👍
So the LCD is 9. ✅
9 is the least common multiple of both denominators. 👏
Great job learning about LCD, or least common denominator.
Now, complete the practice. It'll help you understand more.