Understanding The Least Common Multiple Of 6 And 15

LCM (Least Common Multiple) How to Find LCM? Examples from www.cuemath.com

Introduction

As a professional teacher, it is essential to help students understand the concept of the least common multiple (LCM). This article aims to provide a clear explanation and solution to the problem, "What is the least common multiple of 6 and 15."

What is a Multiple?

Before tackling the concept of LCM, it is crucial to understand what a multiple is. In mathematics, a multiple of a number is the product of that number and any integer. For example, the multiples of 6 are 6, 12, 18, 24, 30, and so on.

What is the Common Multiple?

When dealing with two or more numbers, the common multiple is the product of those numbers and any integer. For instance, the common multiples of 6 and 15 are 30, 60, 90, and so on.

What is the Least Common Multiple?

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more numbers. In other words, it is the smallest number that both 6 and 15 divide into without leaving a remainder.

How to Find the LCM?

There are different methods to find the LCM, but the most common way is to use the prime factorization method. First, we factorize each number into its prime factors. For example, the prime factors of 6 are 2 and 3, while the prime factors of 15 are 3 and 5.

Step 1: Prime Factorization

6 = 2 x 3 15 = 3 x 5

Step 2: Identify Common and Uncommon Factors

We can see that both 6 and 15 have the factor 3 in common. However, 6 has an additional factor of 2, while 15 has an additional factor of 5.

Step 3: Multiply the Factors

To find the LCM, we need to multiply all the factors, including the common and uncommon ones. However, we only need to include each factor once. LCM = 2 x 3 x 5 = 30 Therefore, the LCM of 6 and 15 is 30.

Conclusion

In conclusion, the least common multiple (LCM) is the smallest positive integer that is a multiple of two or more numbers. To find the LCM of 6 and 15, we use the prime factorization method, which involves identifying the common and uncommon factors and multiplying them. The LCM of 6 and 15 is 30.