How to Find the LCM (2 Different Ways) | Least Common Multiple | Math with Mr. J

Summary

In this video, Mr. J explains how to find the least common multiple (LCM) using two methods: listing multiples and prime factorization. He begins with listing multiples, which involves skip counting until a common multiple is found. This method works well for smaller numbers, as shown in examples with 9 and 12, and 10 and 25. For larger numbers, Mr. J demonstrates using prime factorization, breaking numbers down into their prime factors and aligning them to find the LCM. He provides clear, step-by-step explanations and examples to help viewers understand both strategies.

Takeaways

• 🔢 The least common multiple (LCM) is the smallest multiple that two or more numbers share.
• 🧮 A multiple is the result of multiplying a given number by an integer.
• 🔄 One method to find the LCM is by listing out multiples of each number and finding the smallest common multiple.
• 9️⃣ To find the LCM of 9 and 12, the multiples of 9 are 9, 18, 27, 36, and 45, while the multiples of 12 are 12, 24, 36, 48, and 60. The LCM is 36.
• 5️⃣ The LCM of 10 and 25 is found by listing their multiples, 50 being the smallest common multiple.
• 🔍 Another method to find the LCM is using prime factorization, which is more efficient with larger numbers.
• 🧩 In prime factorization, break down each number into its prime factors and match them vertically.
• 📊 For example, the prime factors of 15 are 3 and 5, and the prime factors of 27 are three 3's, making the LCM 135.
• 🔗 For 28 and 52, the prime factors are 2x2x7 for 28 and 2x2x13 for 52. The LCM is 364.
• ✔️ Both strategies (listing multiples and prime factorization) can be useful for finding the LCM depending on the complexity of the numbers involved.

Q & A

What are two strategies mentioned in the video for finding the Least Common Multiple (LCM)?

The two strategies mentioned are listing out multiples and using prime factorization.

How is a multiple defined in the context of finding the LCM?

A multiple is the result of multiplying a given number by an integer. Another way to think of it is by skip counting.

In the first example with the numbers 9 and 12, what is the least common multiple (LCM)?

The least common multiple (LCM) of 9 and 12 is 36.

How many multiples does the video suggest listing to find the LCM?

The video suggests listing four or five multiples of each number to find the LCM.

What is the least common multiple (LCM) of 10 and 25 according to the video?

The least common multiple (LCM) of 10 and 25 is 50.

Why might prime factorization be a better strategy for finding the LCM of larger numbers?

Prime factorization is helpful for larger numbers because listing multiples can be difficult and time-consuming as the numbers increase in value.

What is the prime factorization of 15 as explained in the video?

The prime factorization of 15 is 3 × 5.

What is the prime factorization of 27 as explained in the video?

The prime factorization of 27 is 3 × 3 × 3.

In the example with 15 and 27, what is the least common multiple (LCM) and how is it calculated?

The least common multiple (LCM) of 15 and 27 is 135. It is calculated by multiplying 3 × 5 × 3 × 3.

How does the video calculate the LCM of 28 and 52 using prime factorization?

The prime factorization of 28 is 2 × 2 × 7, and for 52 it is 2 × 2 × 13. The LCM is calculated as 2 × 2 × 7 × 13, which equals 364.