How To Find The LCM of 3 Numbers - Plenty of Examples!

TL;DR

Learn how to find the least common multiple (LCM) using prime factorization to efficiently solve for common multiples of two or more numbers.

Transcript

in this video we're going to focus on finding the least common multiple using prime factorization so let's start with a simple example what is the least common multiple between 3 and 4. so a simple method that you can use is make a list let's start with three so multiples of 3 are 3 6 9 12 15 18 21 24 27 and so forth you can keep adding threes so m... Read More

Key Insights

• 🛩️ The least common multiple is the smallest shared multiple between two or more numbers.
• 👂 Making a list of multiples and identifying common multiples is one approach to finding the LCM.
• ❓ Prime factorization is a more efficient method for determining the LCM.
• ✋ The LCM is found by selecting the highest power of each unique prime factor present in any of the given numbers.

Questions & Answers

Q: What is the least common multiple between 3 and 4?

The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32. The common multiples are 12 and 24, but the least common multiple is 12 since it's the lowest number present in both lists.

Q: How can prime factorization be used to find the LCM?

Prime factorization breaks down a number into its prime factors. For example, the factors of 6 are 3 and 2. To find the LCM, select the highest power of each prime factor present in any of the given numbers. For example, if one number has 3 twos and another has 5 twos, use 2^5, which equals 32.

Q: What is the least common multiple between 24 and 32?

Prime factorization of 24 yields 2^3 * 3, while prime factorization of 32 yields 2^5. Since 24 contains three twos and 32 contains five twos, the LCM is 2^5 * 3 = 96. This can be confirmed by making a list of multiples of 24 and 32.

Q: How do you find the least common multiple between 12, 15, and 20?

Prime factorization of 12: 2^2 * 3, 15: 3 * 5, and 20: 2^2 * 5. The maximum number of twos is 2^2, the maximum number of threes is 3, and the maximum number of fives is 1. Therefore, the LCM is 2^2 * 3 * 5 = 60.

Summary & Key Takeaways

• The least common multiple (LCM) is the smallest multiple that two or more numbers have in common.

• One method to find the LCM is to make a list of multiples for each number and identify common multiples.

• Another method is to use prime factorization to break down the numbers into their prime factors and combine them to find the LCM.

• By using the prime factors and selecting the highest number of each unique factor present in any of the given numbers, you can determine the LCM.