Least common multiple exercise: 3 numbers | Factors and multiples | Pre-Algebra | Khan Academy

TL;DR

The least common multiple (LCM) of 15, 6, and 10 is 30, which is the smallest multiple that is common to all three numbers.

Transcript

What is the least common multiple, abbreviated as LCM, of 15, 6, and 10? So the least common multiple is exactly what the word is saying. It's the least common multiple of these numbers. And I know that probably didn't help you much. But let's actually work through this problem. So to do that, let's just think about the different multiples of the 1... Read More

Key Insights

• 🛩️ The least common multiple is the smallest multiple that is divisible by all the given numbers.
• 👂 Finding the LCM can be done by listing the multiples of each number and finding the smallest common multiple or by using the prime factorization method.
• 🧑‍🏭 The prime factorization method involves breaking down each number into its prime factors and taking the product of all the unique prime factors.
• #️⃣ The prime factorization method is particularly useful for complex numbers.

Questions & Answers

Q: What is the least common multiple of 15, 6, and 10?

The least common multiple of 15, 6, and 10 is 30, which is the smallest multiple that all three numbers divide into evenly.

Q: How are the multiples of each number used to find the LCM?

By listing the multiples of each number and identifying the smallest common multiple, we can determine the LCM. In this case, 30 is the smallest multiple that all three numbers share.

Q: What is the prime factorization method for finding the LCM?

The prime factorization of each number is obtained by breaking it down into its prime factors. The LCM is then determined by multiplying together all the unique prime factors of the given numbers.

Q: Why is the LCM of 15, 6, and 10 equal to 30?

The prime factorization of 15 is 3 x 5, of 6 is 2 x 3, and of 10 is 2 x 5. The LCM must include all of the prime factors, resulting in 2 x 3 x 5 = 30.

Summary & Key Takeaways

• The least common multiple is the smallest multiple that is divisible by all the given numbers.

• One approach to finding the LCM is to list the multiples of each number and identify the smallest common multiple.

• Another method involves determining the prime factorization of each number and taking the product of all the unique prime factors.