Explaining The Least Common Multiple Of 7 And 2

GCF and LCM (videos, worksheets, solutions, activities) from www.onlinemathlearning.com

What is a Multiple?

Before we dive into the concept of the least common multiple, let us first understand what a multiple is. A multiple is a number that can be divided by another number without leaving a remainder. For example, 6 is a multiple of 3 because 3 can divide into 6 evenly without leaving a remainder.

What is the Least Common Multiple?

The least common multiple (LCM) is the smallest multiple that two or more numbers have in common. In other words, it is the smallest number that both numbers can divide into evenly. For example, the LCM of 2 and 3 is 6 because 6 is the smallest number that both 2 and 3 can divide into evenly.

Finding the LCM of 7 and 2

To find the LCM of 7 and 2, we need to find the smallest number that both 7 and 2 can divide into evenly. One way to do this is to list the multiples of both numbers and find the smallest one they have in common. Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105... Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30... Looking at the lists above, we can see that the smallest multiple that both 7 and 2 have in common is 14. Therefore, the LCM of 7 and 2 is 14.

Why is the LCM Important?

The LCM is an important concept in mathematics because it is used in a variety of applications such as adding and subtracting fractions, simplifying radicals, and solving algebraic equations. Without the LCM, it would be difficult to solve many math problems.

Using Prime Factorization to Find the LCM

Another way to find the LCM of two or more numbers is to use prime factorization. Prime factorization is the process of breaking down a number into its prime factors. To find the LCM using prime factorization, we need to follow these steps: 1. Write each number as a product of its prime factors. 2. Identify the common factors and write them down once. 3. Multiply the common factors together to get the LCM. Let's use this method to find the LCM of 7 and 2: Prime factors of 7: 7 (7 is a prime number) Prime factors of 2: 2 (2 is a prime number) Since there are no common factors, the LCM is simply the product of the two numbers: 7 x 2 = 14.

Conclusion

In conclusion, the least common multiple is the smallest multiple that two or more numbers have in common. To find the LCM of 7 and 2, we can list their multiples or use prime factorization. The LCM is an important concept in mathematics and is used in many applications.