Explaining The Least Common Multiple Of 3 And 9

What is the least common multiple of 3 and 9? Socratic from socratic.org

What is a Multiple?

Before we dive into the least common multiple of 3 and 9, we must first understand what a multiple is. A multiple is a product of a number and any other whole number. For example, the first few multiples of 3 are 3, 6, 9, 12, 15, and so on.

What is the Least Common Multiple?

The least common multiple, or LCM for short, is the smallest multiple that two or more numbers have in common. In this case, we are looking for the smallest multiple that both 3 and 9 share.

How to Find the LCM of 3 and 9

There are a few methods to find the LCM of 3 and 9, but we will focus on the most common one - prime factorization. To do this, we need to break down each number into its prime factors.

Prime Factorization of 3

The number 3 is a prime number, which means it can only be divided by 1 and itself. Therefore, its prime factorization is simply 3.

Prime Factorization of 9

The number 9, on the other hand, is not a prime number. It can be divided by 3, which gives us 3 x 3. Therefore, its prime factorization is 3 x 3.

Putting it Together

Now that we have the prime factorization of both numbers, we can find their LCM by taking the highest power of each prime factor. In this case, the highest power of 3 is 3 x 3, which gives us 9. Therefore, the LCM of 3 and 9 is 9.

Why is the LCM Useful?

The LCM is useful in many mathematical applications, such as adding and subtracting fractions with different denominators. In order to do this, we need to find the LCM of the denominators and convert the fractions to have the same denominator.

In Conclusion

In summary, the least common multiple of 3 and 9 is 9. We found this by breaking down each number into its prime factors and taking the highest power of each. The LCM is a useful tool in many mathematical applications, such as adding and subtracting fractions.