Select The Best Answer For The Question.What Is The Least Common Multiple Of $3, 4, 6,$ And $8$?A. 24 B. 8 C. 72 D. 96

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Understanding the Concept of Least Common Multiple (LCM)

The least common multiple (LCM) is a fundamental concept in mathematics that plays a crucial role in various mathematical operations, including addition, subtraction, multiplication, and division. In this article, we will delve into the concept of LCM and explore how to find the LCM of a set of numbers.

What is the Least Common Multiple (LCM)?

The LCM of a set of numbers is the smallest number that is a multiple of each of the numbers in the set. In other words, it is the smallest number that can be divided evenly by each of the numbers in the set. For example, the LCM of 2, 3, and 4 is 12, because 12 is the smallest number that can be divided evenly by 2, 3, and 4.

Finding the LCM of a Set of Numbers

To find the LCM of a set of numbers, we can use the following steps:

  1. List the multiples of each number: Start by listing the multiples of each number in the set.
  2. Identify the common multiples: Identify the numbers that are common to all the lists of multiples.
  3. Find the smallest common multiple: Find the smallest number that is common to all the lists of multiples.

Finding the LCM of 3, 4, 6, and 8

To find the LCM of 3, 4, 6, and 8, we can use the steps outlined above.

Step 1: List the Multiples of Each Number

  • Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
  • Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...
  • Multiples of 6: 6, 12, 18, 24, 30, 36, ...
  • Multiples of 8: 8, 16, 24, 32, 40, ...

Step 2: Identify the Common Multiples

From the lists of multiples, we can see that the common multiples of 3, 4, 6, and 8 are 24, 48, 72, and so on.

Step 3: Find the Smallest Common Multiple

The smallest common multiple of 3, 4, 6, and 8 is 24.

Conclusion

In conclusion, the LCM of 3, 4, 6, and 8 is 24. This means that 24 is the smallest number that can be divided evenly by 3, 4, 6, and 8.

Answer

The correct answer is A. 24.

Why is the LCM Important?

The LCM is an important concept in mathematics because it plays a crucial role in various mathematical operations, including addition, subtraction, multiplication, and division. For example, when we add or subtract fractions, we need to find the LCM of the denominators to ensure that the fractions have a common denominator.

Real-World Applications of LCM

The LCM has many real-world applications, including:

  • Music: In music, the LCM is used to find the common time signature of two or more melodies.
  • Science: In science, the LCM is used to find the common unit of measurement of two or more quantities.
  • Finance: In finance, the LCM is used to find the common interest rate of two or more investments.

Common Mistakes to Avoid

When finding the LCM of a set of numbers, there are several common mistakes to avoid, including:

  • Not listing all the multiples: Failing to list all the multiples of each number can lead to incorrect results.
  • Not identifying the common multiples: Failing to identify the common multiples can lead to incorrect results.
  • Not finding the smallest common multiple: Failing to find the smallest common multiple can lead to incorrect results.

Tips and Tricks

Here are some tips and tricks to help you find the LCM of a set of numbers:

  • Use a calculator: Using a calculator can help you find the LCM quickly and accurately.
  • List the multiples in order: Listing the multiples in order can help you identify the common multiples more easily.
  • Use the prime factorization method: Using the prime factorization method can help you find the LCM more easily.

Conclusion

In conclusion, the LCM is an important concept in mathematics that plays a crucial role in various mathematical operations. Finding the LCM of a set of numbers requires careful attention to detail and a thorough understanding of the concept. By following the steps outlined above and avoiding common mistakes, you can find the LCM of a set of numbers quickly and accurately.
Q&A: Least Common Multiple (LCM)

In this article, we will answer some frequently asked questions about the least common multiple (LCM).

Q: What is the LCM of two numbers?

A: The LCM of two numbers is the smallest number that is a multiple of both numbers.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, you can use the following steps:

  1. List the multiples of each number: Start by listing the multiples of each number.
  2. Identify the common multiples: Identify the numbers that are common to both lists of multiples.
  3. Find the smallest common multiple: Find the smallest number that is common to both lists of multiples.

Q: What is the LCM of 12 and 15?

A: To find the LCM of 12 and 15, we can use the steps outlined above.

Step 1: List the Multiples of Each Number

  • Multiples of 12: 12, 24, 36, 48, 60, ...
  • Multiples of 15: 15, 30, 45, 60, 75, ...

Step 2: Identify the Common Multiples

From the lists of multiples, we can see that the common multiples of 12 and 15 are 60, 120, 180, and so on.

Step 3: Find the Smallest Common Multiple

The smallest common multiple of 12 and 15 is 60.

Q: What is the LCM of 24 and 36?

A: To find the LCM of 24 and 36, we can use the steps outlined above.

Step 1: List the Multiples of Each Number

  • Multiples of 24: 24, 48, 72, 96, 120, ...
  • Multiples of 36: 36, 72, 108, 144, 180, ...

Step 2: Identify the Common Multiples

From the lists of multiples, we can see that the common multiples of 24 and 36 are 72, 144, 216, and so on.

Step 3: Find the Smallest Common Multiple

The smallest common multiple of 24 and 36 is 72.

Q: What is the LCM of 48 and 60?

A: To find the LCM of 48 and 60, we can use the steps outlined above.

Step 1: List the Multiples of Each Number

  • Multiples of 48: 48, 96, 144, 192, 240, ...
  • Multiples of 60: 60, 120, 180, 240, 300, ...

Step 2: Identify the Common Multiples

From the lists of multiples, we can see that the common multiples of 48 and 60 are 240, 480, 720, and so on.

Step 3: Find the Smallest Common Multiple

The smallest common multiple of 48 and 60 is 240.

Q: What is the LCM of 72 and 90?

A: To find the LCM of 72 and 90, we can use the steps outlined above.

Step 1: List the Multiples of Each Number

  • Multiples of 72: 72, 144, 216, 288, 360, ...
  • Multiples of 90: 90, 180, 270, 360, 450, ...

Step 2: Identify the Common Multiples

From the lists of multiples, we can see that the common multiples of 72 and 90 are 360, 720, 1080, and so on.

Step 3: Find the Smallest Common Multiple

The smallest common multiple of 72 and 90 is 360.

Conclusion

In conclusion, the LCM is an important concept in mathematics that plays a crucial role in various mathematical operations. By following the steps outlined above and using the prime factorization method, you can find the LCM of a set of numbers quickly and accurately.

Frequently Asked Questions

Here are some frequently asked questions about the LCM:

  • Q: What is the LCM of two numbers? A: The LCM of two numbers is the smallest number that is a multiple of both numbers.
  • Q: How do I find the LCM of two numbers? A: To find the LCM of two numbers, you can use the following steps:
    1. List the multiples of each number: Start by listing the multiples of each number.
    2. Identify the common multiples: Identify the numbers that are common to both lists of multiples.
    3. Find the smallest common multiple: Find the smallest number that is common to both lists of multiples.
  • Q: What is the LCM of 12 and 15? A: The LCM of 12 and 15 is 60.
  • Q: What is the LCM of 24 and 36? A: The LCM of 24 and 36 is 72.
  • Q: What is the LCM of 48 and 60? A: The LCM of 48 and 60 is 240.
  • Q: What is the LCM of 72 and 90? A: The LCM of 72 and 90 is 360.

Common Mistakes to Avoid

When finding the LCM of a set of numbers, there are several common mistakes to avoid, including:

  • Not listing all the multiples: Failing to list all the multiples of each number can lead to incorrect results.
  • Not identifying the common multiples: Failing to identify the common multiples can lead to incorrect results.
  • Not finding the smallest common multiple: Failing to find the smallest common multiple can lead to incorrect results.

Tips and Tricks

Here are some tips and tricks to help you find the LCM of a set of numbers:

  • Use a calculator: Using a calculator can help you find the LCM quickly and accurately.
  • List the multiples in order: Listing the multiples in order can help you identify the common multiples more easily.
  • Use the prime factorization method: Using the prime factorization method can help you find the LCM more easily.

Conclusion

In conclusion, the LCM is an important concept in mathematics that plays a crucial role in various mathematical operations. By following the steps outlined above and using the prime factorization method, you can find the LCM of a set of numbers quickly and accurately.