To find the least common denominator (LCD) of two or more numbers, we use prime factorization.
To do so, we follow these steps:
0. We arrange our numbers in a straight line
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1. We'll start with the first prime number: 2. If any of our numbers can be divided by two, we divide it. If some numbers aren't, we leave such number as is. If none are divisble by 2, we'll move on
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2. If none of the resulting numbers from step two are still divisible by 2, we repeat the step with the next prime number: 3. If none of the resulting numbers are still divisible by 3, we continue with the next prime number.
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3. We repeat these steps with the following prime numbers, until all of our numbers are reduced to 1.
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4. We take all the prime numbers we used and multiply them. If we used a number more than once, we multilpy by it as many times as we used it.
Now, let's take a look at an example:
Let's find the LCD between 6, 9, and 3. We'll do it step by step.
First, we'll arrange them:
6 9 3
Now, we start with the first prime number: 2. One of our numbers is divisible by 2, so we divide it.
3 9 3
We continue with three. We divide our numbers by 3:
1 3 1
One of our numbers can still be divided by 3, so we divide that number again.
1 1 1
All of our numbers are ones. Now we take a look at the prime numbers we used:
• We used ,2, just once
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• We used ,3, two times
We multiply to get our LCD:
Therefore, the least common denominator between 6, 9 and 3 is 18