Equivalent Fractions: Least Common Multiple (LCM) - Fast And Easy Math Learning Videos
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Title: Equivalent Fractions: Least Common Multiple (LCM)
You already know one way to find a common denominator for any two fractions and one way to find a common denominator for some fractions. In this and the next lesson, you’ll learn another way to find a common denominator for any two fractions. This method uses what is called the least common multiple. In this lesson, you’ll learn to find the least common multiple for two numbers. In the next lesson, you’ll learn to use the least common multiple as the common denominator for two fractions.
Consider these two numbers, 6 and 4. We want to find the smallest number that’s a multiple of each of these numbers. Let’s look at these numbers on a number line.
Let’s start with the multiples of 6. Six times one is 6.
Six times 2 is 12.
Six times 3 is 18.
Six times 4 is 24.
Now let’s look at the multiples of 4. Four times one is 4.
Four times 2 is 8.
Four times 3 is 12.
Four times 4 is 16.
Four times 5 is 20.
Four times 6 is 24.
Notice that there are two places where the multiples of 4 and 6 are the same. The first one is here, at 12.
Twelve is a multiple of both 6 and 4.
The second place where multiples of 4 and 6 are the same is here, at 24.
For our purposes, what we want is the smallest number that’s a multiple of both 6 and 4. That number is 12.
We call this the “least common multiple” of 6 and 4.
We can also find the least common multiple of two numbers without using a number line. Here’s an example, 5 and 4. First, we list several multiples of 5 in order:
Now we list several multiples of 4 in order.
We can see that there’s a common multiple, which is 20.
Since this is the smallest number that’s a multiple of both 5 and 4, this is the least common multiple.
Another example, 6 and 9. First, we list several multiples of 6
Next, we list several multiples of 9.
The smallest number that’s a multiple of both 6 and 9 is 18.
Last example, 2 and 9. First, we list multiples of 2.
Then we list multiples of 9.
The smallest number that’s a multiple of both 2 and 9 is 18.
In the remainder of this lesson, you’ll find the least common multiple of two numbers like these.
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