Ana Is Pedro Are Organizing A Composition At School. They Want The Lanes That Each One Run At Some Point So They Can Start And Finish Together. The Track Ana Uses Is 60 Meters Long. What Is The Smallest

by ADMIN 203 views

Introduction

Ana and Pedro are organizing a composition at school, and they want to make sure that they can start and finish together at some point. To achieve this, they need to find the smallest common multiple of the lengths of the tracks they will be running on. In this article, we will explore how to find the smallest common multiple of two numbers, and we will apply this concept to Ana and Pedro's situation.

What is the Smallest Common Multiple?

The smallest common multiple (SCM) of two numbers is the smallest number that is a multiple of both numbers. In other words, it is the smallest number that can be divided evenly by both numbers. For example, the SCM of 4 and 6 is 12, because 12 is the smallest number that can be divided evenly by both 4 and 6.

Finding the Smallest Common Multiple

To find the SCM of two numbers, we can use the following steps:

  1. List the multiples of each number: Start by listing the multiples of each number. For example, if we want to find the SCM of 4 and 6, we can list the multiples of 4 as 4, 8, 12, 16, 20, ... and the multiples of 6 as 6, 12, 18, 24, 30, ...
  2. Identify the smallest common multiple: Once we have listed the multiples of each number, we can identify the smallest number that appears in both lists. In the example above, the smallest common multiple of 4 and 6 is 12.
  3. Verify the result: To make sure that we have found the correct SCM, we can verify that it can be divided evenly by both numbers. In the example above, we can see that 12 can be divided evenly by both 4 and 6.

Ana and Pedro's Situation

Ana and Pedro are running on tracks that are 60 meters long. To find the smallest common multiple of the lengths of their tracks, we can use the steps outlined above.

Step 1: List the Multiples of Each Number

The multiples of 60 are: 60, 120, 180, 240, 300, ...

The multiples of 60 are: 60, 120, 180, 240, 300, ...

Step 2: Identify the Smallest Common Multiple

The smallest common multiple of 60 and 60 is 60.

Step 3: Verify the Result

To make sure that we have found the correct SCM, we can verify that it can be divided evenly by both numbers. In this case, we can see that 60 can be divided evenly by both 60 and 60.

Conclusion

In this article, we have explored how to find the smallest common multiple of two numbers. We have applied this concept to Ana and Pedro's situation, and we have found that the smallest common multiple of the lengths of their tracks is 60 meters.

The Importance of the Smallest Common Multiple

The smallest common multiple is an important concept in mathematics, and it has many practical applications. For example, it can be used to find the least common multiple of two or more numbers, which is useful in a variety of situations, such as music composition, where the least common multiple of two or more time signatures can be used to determine the tempo of a piece.

Real-World Applications of the Smallest Common Multiple

The smallest common multiple has many real-world applications, including:

  • Music composition: The least common multiple of two or more time signatures can be used to determine the tempo of a piece.
  • Computer science: The smallest common multiple can be used to find the least common multiple of two or more numbers, which is useful in algorithms and data structures.
  • Engineering: The smallest common multiple can be used to find the least common multiple of two or more frequencies, which is useful in signal processing and filtering.

Conclusion

Q&A: Smallest Common Multiple

Q: What is the smallest common multiple (SCM)? A: The smallest common multiple (SCM) of two numbers is the smallest number that is a multiple of both numbers. In other words, it is the smallest number that can be divided evenly by both numbers.

Q: How do I find the smallest common multiple of two numbers? A: To find the SCM 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 smallest common multiple: Once you have listed the multiples of each number, identify the smallest number that appears in both lists.
  3. Verify the result: To make sure that you have found the correct SCM, verify that it can be divided evenly by both numbers.

Q: What is the difference between the smallest common multiple and the least common multiple? A: The smallest common multiple (SCM) and the least common multiple (LCM) are often used interchangeably, but they are not exactly the same thing. The SCM is the smallest number that is a multiple of both numbers, while the LCM is the smallest number that is a multiple of both numbers and is also a multiple of any other common multiple.

Q: How do I find the least common multiple 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 least common multiple: Once you have listed the multiples of each number, identify the smallest number that appears in both lists.
  3. Verify the result: To make sure that you have found the correct LCM, verify that it can be divided evenly by both numbers.

Q: What are some real-world applications of the smallest common multiple? A: The smallest common multiple has many real-world applications, including:

  • Music composition: The least common multiple of two or more time signatures can be used to determine the tempo of a piece.
  • Computer science: The smallest common multiple can be used to find the least common multiple of two or more numbers, which is useful in algorithms and data structures.
  • Engineering: The smallest common multiple can be used to find the least common multiple of two or more frequencies, which is useful in signal processing and filtering.

Q: Can I use a calculator to find the smallest common multiple? A: Yes, you can use a calculator to find the smallest common multiple. Many calculators have a built-in function for finding the least common multiple, which can save you time and effort.

Q: What if I have three or more numbers and I want to find the smallest common multiple? A: If you have three or more numbers and you want to find the smallest common multiple, you can use the same steps as before, but you will need to list the multiples of each number and identify the smallest number that appears in all lists.

Q: Can I use a formula to find the smallest common multiple? A: Yes, you can use a formula to find the smallest common multiple. The formula for the smallest common multiple of two numbers is:

SCM(a, b) = (a × b) / gcd(a, b)

where gcd(a, b) is the greatest common divisor of a and b.

Conclusion

In conclusion, the smallest common multiple is an important concept in mathematics, and it has many practical applications. We have explored how to find the smallest common multiple of two numbers, and we have answered some common questions about this concept.