## Greatest Common Factor and Least Common Multiple

#### Aligned To Common Core Standard:

**Grade 6 Numbers** - 6.NS.B.4

What is the Greatest Common Factor and Least Common Multiple?
They both fall under the umbrella of Factorization. Let us discuss both of these terms individually.
**Least Common Multiple (LCM)** -
A common multiple is a number which is a multiple of two or more than two numbers. The least common multiple of two numbers is the smallest number which is the multiple of both of the numbers mentioned above. LCM can be found out by multiplying one of the two numbers by the prime factors of the second number; that the two numbers do not have two prime factors collectively. Let us consider an example 16 and 24, who’s prime factors are as follows.
16 = 2 x 2 x 2 x 2
24 = 2 x 2 x 2 x 3
The number which is different in all the common prime factors is 3. So, we multiply 16 by three and the LCM of both numbers becomes 48.
**Greatest Common Factor (GCF)** -
The greatest common factor is defined as the greatest factor, which found within two or more numbers. In other words, if we have to find the GCF of 16 and 24, we will follow the steps given below.
16 = 2 x 2 x 2 x 2
24 = 2 x 2 x 2 x 3
Now, we see that three factors are common in both numbers, which are also underlined. The product of these three numbers is 2 x 2 x 2 = 8. The GCF 16 and 24 is 8.

### Printable Worksheets And Lessons

- GCF and LCM Step-by-step
Lesson- We go over both skills in detail. You will learn when they are used and how to find them.

- Guided Lesson - The skill is stepped up just a bit because we introduce finding the GCF and LCM between 3 numbers.
- Guided Lesson Explanation - Yeah, I get it! I went a little overboard with the explanation on this, but kids usually get it when they see it this way.
- Practice Worksheet - Kind of a drill and kill worksheet on the two skills. This is our most popular worksheet in this section.
- Common Factors Five Pack - This pack of five worksheets will help you with exercises that have you determine both the GCF and LCM of values.
- Least Common Multiple Five Pack - 50 lcm problems for you to take by the horns.
- Matching Worksheet - This just picks up where the practice sheet left off. More practice can never hurt!

#### Homework Sheets

Each sheet works on an individual skill. In this case, we focus on GCF twice and LCM once.

- Homework 1 - We know that the greatest common factor is the greatest whole number that is a factor of each of the numbers.
- Homework 2 - List the multiples of each number. Find the lowest number that appears in both lists.
- Homework 3 - The greatest common factor of 12, 9, and 3 is _____.

#### Practice Worksheets

I put my own unique twist on these for you. This will help you learn both skills quickly.

- Practice 1 - What is the least common multiple of: 5, 10, 15
- Practice 2 - What is the greatest common factor of these integers? 15 and 35
- Practice 3 - A mix of GCF and LCM problems. To see where you sit with this skill.

#### Math Skill Quizzes

We bounce between the different skills set forth by the standard here. These quizzes are really good for seeing how well you know this skill.

- Quiz 1 - Find the GCF of 16 and 20. Look for commonality in the values.
- Quiz 2 - What is the LCM of 8 and 12?
- Quiz 3 - What is the GCF of these three integers? 12, 14, 16. Work through all the values you can think of mentally.

### When Do We Use This Calculation in The Real World?

The GCF is used in situations where you need to break up things into smaller pieces. It can also be used to equally scatter groups of items into larger groups. One of the most common applications of this is to place things into rows and columns, like a spreadsheet. We almost subconsciously use this skill to help us simply fractions, especially in ratios. In fact, this skill is the fundamental ratio math. The LCM helps us evaluate things that are repeating multiple times. This helps us both predict repeating behavior or exploring and explaining commonalities between two separate events. This lends itself to being a way to calculate fairness in distribution. This is what we would use to make sure we were evenly distribute snacks at a party when you have a greater population in one area of the party and smaller crowd in another area. This skill has countless applications and this one situation that it fits. Both of these techniques are used by most adults every day. If you ever shop in a grocery store and are trying to determine what the best deal is, remember this big time!