How To Find The LCM of 3 Numbers - Plenty of Examples!
TLDRThis educational video script teaches the method of finding the least common multiple (LCM) using prime factorization. It walks through examples with pairs and groups of numbers, showing how to list multiples and identify LCMs. The script also demonstrates the prime factorization process for numbers like 6, 9, 24, 32, and others, explaining how to combine the highest powers of prime factors to determine the LCM efficiently. The video concludes with a step-by-step guide for finding the LCM of four numbers, reinforcing the concept with a practical approach.
Takeaways
- 🔢 The video explains how to find the Least Common Multiple (LCM) using prime factorization.
- 📝 The first example given is finding the LCM of 3 and 4, which is 12, by listing multiples and identifying common ones.
- 📚 The second example demonstrates the LCM of 6 and 9, which is 18, using both listing and prime factorization methods.
- 📈 Prime factorization involves breaking down numbers into their prime factors to find the LCM, as shown with the 6 and 9 example.
- 📉 For the 24 and 32 example, the LCM is calculated using prime factors, resulting in 96, and then verified by listing multiples.
- 📌 The importance of using the highest count of each prime factor from the given numbers to determine the LCM is emphasized.
- 🔑 The script shows how to find the LCM of three numbers (12, 15, and 20) by using their prime factors, resulting in 60.
- 📝 The process of verifying the LCM by dividing it by each of the original numbers to ensure whole number results is highlighted.
- 📈 An example with four numbers (8, 10, 12, and 15) is used to illustrate the LCM calculation, which turns out to be 120.
- 📚 The final example reinforces the method of using the greatest number of each prime factor to calculate the LCM of multiple numbers.
- 📝 The video concludes by summarizing the process and encouraging viewers to practice making lists to verify the LCM of numbers.
Q & A
What is the least common multiple (LCM) between 3 and 4?
-The least common multiple between 3 and 4 is 12, as it is the smallest number that appears in both the multiples of 3 and the multiples of 4.
How do you find the LCM of 6 and N using the method demonstrated in the video?
-To find the LCM of 6 and N, list the multiples of each number and identify the smallest number that appears in both lists. For 6, the multiples are 6, 12, 18, 24, etc., and for N, you would continue the pattern based on N's value. The LCM is the smallest common multiple.
What is the LCM of 6 and 9 using prime factorization?
-The prime factors of 6 are 2 and 3, and for 9, they are 3 and 3. The LCM is found by multiplying the highest powers of all prime factors present in either number, which in this case is 2 * 3 * 3, resulting in 18.
How can you determine the LCM of 24 and 32 using prime factorization?
-The prime factors for 24 are 2, 2, and 3, and for 32, they are 2, 2, 2, 2, and 2. The LCM is found by using the highest powers of all prime factors present, which is 3 * (2^5), resulting in 96.
What is the LCM of 12, 15, and 20, and how do you find it using prime factorization?
-The LCM of 12, 15, and 20 is 60. To find it, list the prime factors of each number: 12 has 2, 2, and 3; 15 has 3 and 5; 20 has 2, 2, and 5. The LCM is the product of the highest powers of all prime factors, which is 2^2 * 3 * 5, equaling 60.
How do you prove that 96 is the LCM of 24 and 32 by making a list?
-To prove that 96 is the LCM, list the multiples of 24 and 32. The multiples of 24 are 24, 48, 72, and 96, and for 32, they are 32, 64, and 96. Since 96 appears in both lists and is the highest number, it is the LCM.
What is the LCM of 8, 10, 12, and 15, and how do you find it using prime factorization?
-The LCM of 8, 10, 12, and 15 is 120. Using prime factorization, 8 has 2, 2, and 2; 10 has 2 and 5; 12 has 2, 2, and 3; and 15 has 3 and 5. The LCM is found by multiplying the highest powers of all prime factors, which is 2^3 * 3 * 5, resulting in 120.
Why is it necessary to use the highest powers of prime factors when finding the LCM?
-Using the highest powers of prime factors ensures that the LCM is the smallest number that all the given numbers divide into without leaving a remainder, as it includes all prime factors necessary for each number to be divisible by the LCM.
Can you find the LCM of numbers without prime factorization?
-Yes, you can find the LCM without prime factorization by listing the multiples of each number and identifying the smallest common multiple. However, prime factorization is a more efficient method, especially for larger numbers.
What is the significance of the LCM in mathematics and real-life applications?
-The LCM is significant in mathematics for solving problems involving divisibility and ratios. In real life, it is used in various applications such as scheduling, determining the size of materials needed for construction, and in music for finding the least common beat.
Outlines
🔢 Finding the Least Common Multiple (LCM) Through Prime Factorization
This paragraph introduces the concept of finding the least common multiple (LCM) using prime factorization. It begins with a simple example using the numbers 3 and 4, demonstrating how to list multiples and identify the LCM. The method is then applied to the numbers 6 and 9, explaining the process of using prime factors to find the LCM. The paragraph emphasizes the importance of selecting the highest number of each prime factor found in the given numbers to calculate the LCM. The process is illustrated with step-by-step instructions, making it accessible for viewers to understand and follow.
📈 Applying Prime Factorization to Calculate LCM for Multiple Numbers
The second paragraph delves into the application of prime factorization to determine the LCM for pairs of numbers, such as 24 and 32. It explains how to break down each number into its prime factors and then select the highest occurrences of these factors to find the LCM. The paragraph provides a step-by-step guide on multiplying the chosen prime factors to arrive at the LCM, which in this case is 96. Additionally, it offers a verification method by dividing the LCM by the original numbers to ensure whole number results, confirming 96 as the correct LCM. The paragraph also challenges viewers to find the LCM for the numbers 12, 15, and 20, guiding them through the prime factorization process and revealing the LCM to be 60.
📚 Expanding LCM Calculation to Include Four Numbers
The final paragraph extends the LCM calculation to include four numbers: 8, 10, 12, and 15. It begins by breaking down each number into its prime factors, identifying the highest occurrences of each prime factor across the numbers. The paragraph then demonstrates how to multiply these prime factors to find the LCM, which is calculated to be 120. To validate this result, the paragraph suggests checking divisibility by each of the original numbers. The conclusion of the video is a reminder of the method for creating a list of multiples to verify the LCM, offering a comprehensive overview of the process and its application to various numbers.
Mindmap
Keywords
💡Least Common Multiple (LCM)
💡Prime Factorization
💡Multiples
💡Common Multiple
💡Factors
💡Divisibility
💡Composite Number
💡Power of a Prime
💡Verification
💡List
Highlights
Introduction to finding the least common multiple (LCM) using prime factorization.
Simple example of finding LCM between 3 and 4 using multiples list.
Identification of 12 as the LCM for 3 and 4 through the multiples list method.
Exploration of LCM for 6 and N, encouraging viewers to pause and solve.
Demonstration of LCM calculation for 6 and 9 using prime factorization.
Explanation of using the highest count of prime factors from either number to find LCM.
Example of finding LCM between 24 and 32 using both list method and prime factorization.
Prime factorization of 24 and 32 and the process of determining LCM using these factors.
Verification of LCM (96) for 24 and 32 by division and multiples list.
Challenge to find LCM for 12, 15, and 20 with a pause for viewer participation.
Prime factorization of 12, 15, and 20 and the method to determine their LCM.
Calculation of LCM for 12, 15, and 20 resulting in 60.
Verification of 60 as the LCM for 12, 15, and 20 using division and multiples list.
Introduction of a more complex example with four numbers: 8, 10, 12, and 15.
Prime factorization of 8, 10, 12, and 15 for finding their LCM.
Calculation of LCM for 8, 10, 12, and 15 resulting in 120.
Verification of 120 as the LCM for 8, 10, 12, and 15 using division.
Conclusion of the video with a summary of the process and a thank you note.
Transcripts
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