What Is The Lowest Common Multiple (LCM) Of 3, 9, And 15?A. 3 B. 27 C. 45 D. 90

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Introduction to LCM

The lowest common multiple (LCM) is a fundamental concept in mathematics that plays a crucial role in various mathematical operations, including algebra, geometry, and number theory. In simple terms, the LCM of a set of numbers is the smallest number that is a multiple of each of the numbers in the set. In this article, we will explore the concept of LCM and determine the LCM of 3, 9, and 15.

Understanding the Concept of LCM

To understand the concept of LCM, let's consider an example. Suppose we have two numbers, 4 and 6. The multiples of 4 are 4, 8, 12, 16, 20, 24, and so on. The multiples of 6 are 6, 12, 18, 24, 30, and so on. As we can see, the smallest number that is a multiple of both 4 and 6 is 12. Therefore, the LCM of 4 and 6 is 12.

Finding the LCM of 3, 9, and 15

To find the LCM of 3, 9, and 15, we need to list the multiples of each number and find the smallest number that is a multiple of all three numbers.

Multiples of 3

The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, and so on.

Multiples of 9

The multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and so on.

Multiples of 15

The multiples of 15 are 15, 30, 45, 60, 75, 90, and so on.

Determining the LCM

As we can see from the lists above, the smallest number that is a multiple of all three numbers is 45. Therefore, the LCM of 3, 9, and 15 is 45.

Conclusion

In conclusion, the LCM of 3, 9, and 15 is 45. This is because 45 is the smallest number that is a multiple of all three numbers. Understanding the concept of LCM is essential in various mathematical operations, and it is a fundamental concept in mathematics.

Frequently Asked Questions

  • What is the LCM of 4 and 6?
  • The LCM of 4 and 6 is 12.
  • What is the LCM of 3, 9, and 15?
  • The LCM of 3, 9, and 15 is 45.

Final Answer

The final answer is C. 45.

Introduction

The lowest common multiple (LCM) is a fundamental concept in mathematics that plays a crucial role in various mathematical operations, including algebra, geometry, and number theory. In this article, we will answer some frequently asked questions about LCM and provide a comprehensive understanding of this concept.

Q&A

Q1: What is the LCM of 4 and 6?

A1: The LCM of 4 and 6 is 12.

Q2: How do I find the LCM of two numbers?

A2: To find the LCM of two numbers, you need to list the multiples of each number and find the smallest number that is a multiple of both numbers.

Q3: What is the LCM of 3, 9, and 15?

A3: The LCM of 3, 9, and 15 is 45.

Q4: How do I find the LCM of three or more numbers?

A4: To find the LCM of three or more numbers, you need to list the multiples of each number and find the smallest number that is a multiple of all the numbers.

Q5: What is the difference between LCM and Greatest Common Divisor (GCD)?

A5: The LCM and GCD are two related but distinct concepts in mathematics. The GCD is the largest number that divides both numbers without leaving a remainder, while the LCM is the smallest number that is a multiple of both numbers.

Q6: How do I use LCM in real-life situations?

A6: LCM is used in various real-life situations, such as calculating the time it takes for two or more people to complete a task, determining the amount of material needed for a project, and calculating the cost of a product.

Q7: Can you give an example of how to find the LCM of two numbers?

A7: Let's say we want to find the LCM of 8 and 12. The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, and so on. The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, and so on. As we can see, the smallest number that is a multiple of both 8 and 12 is 24. Therefore, the LCM of 8 and 12 is 24.

Q8: Can you give an example of how to find the LCM of three numbers?

A8: Let's say we want to find the LCM of 6, 8, and 12. The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, and so on. The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, and so on. The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, and so on. As we can see, the smallest number that is a multiple of all three numbers is 24. Therefore, the LCM of 6, 8, and 12 is 24.

Conclusion

In conclusion, the LCM is a fundamental concept in mathematics that plays a crucial role in various mathematical operations. Understanding the concept of LCM is essential in various real-life situations, and it is a fundamental concept in mathematics.

Frequently Asked Questions

  • What is the LCM of 4 and 6?
  • The LCM of 4 and 6 is 12.
  • How do I find the LCM of two numbers?
  • To find the LCM of two numbers, you need to list the multiples of each number and find the smallest number that is a multiple of both numbers.
  • What is the LCM of 3, 9, and 15?
  • The LCM of 3, 9, and 15 is 45.

Final Answer

The final answer is C. 45.