# How can you find the least common multiple using prime factorization?

See process below:

Let's come up with a problem so that I can show you the process.

What is the least common multiple of 12 and 9?

Let's prime factor each of the numbers:

12's prime factors are

9's prime factors are

Now make a chart with both of the numbers:

This is where it gets a little tricky. What we're going to is find the lowest number in our prime factorization. That number is

Obviously, 12 has more 2's because 9 has none.

Now what's the other number in our prime factorization?

9 has more 3's than 12, so I am going to cross out the other 3. We only want the part with the most threes.

Put all of the highlighted numbers down into one multiplication problem:

36 is the least common multiple between 12 and 9.

This is a really helpful video on YouTube about this topic:least common multiple

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To find the least common multiple (LCM) using prime factorization, follow these steps:

- Write the prime factorization of each number.
- Identify all the unique prime factors from both sets of prime factorizations.
- For each prime factor, take the highest power it appears with in either of the numbers' prime factorizations.
- Multiply all these prime factors together to get the LCM.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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