Back To Course

6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, you will learn what kinds of word problems you can expect to see that involve the greatest common factor or the least common multiple. Learn what you need to do to understand these problems and then to solve them.

Word problems, here we go! Yes, in this video lesson, we will be learning about word problems. Now, don't get all worried. I know that word problems are sometimes the hardest part of math. But I'll show you how you can solve these word problems without breaking your brain.

The first type of word problem that we will consider in this video lesson is the one that involves the **greatest common factor**, the greatest common factor that is shared between two or more numbers. For example, the number 3 is the greatest common factor between 9 and 6 because both can be divided equally by 3. There is no higher number that can be divided equally between 9 and 6.

When you come across a word problem that involves the greatest common factor, you might see a problem like this one:

'Farmer John and Farmer Jane are planning out their fruit orchard. Farmer John is planting the orange trees, and Farmer Jane is planting the cherry trees. Farmer John has 30 orange trees to plant, and Farmer Jane has 24 cherry trees to plant. They want to plant the trees so that each row has the same number of trees. What is the largest number of trees each row can have?'

This problem is a greatest common factor word problem because it is asking you to find the greatest common factor between the numbers 30 and 24. The greatest common factor in our word problem translates to the number of trees in each row. Do you remember how to find the greatest common factor? The easiest method is to write out all the factors for each number. Then, we compare the factors and find the greatest factor that they both have in common.

So, the number 30 has the factors 1, 2, 3, 5, 6, 10, 15, and 30. The number 24 has the factors 1, 2, 3, 4, 6, 8, 12, and 24. Now, which of these numbers do they have in common? They have 1, 2, 3, and 6 in common. Which one is the greatest? 6 is the greatest, so 6 is the greatest common factor; that means 6 is our answer. We can have a maximum of 6 trees in each row of the fruit orchard so that all the rows are the same number.

The next type of word problem we will consider in this video lesson is the one involving the **least common multiple**, the smallest multiple shared between two numbers. For example, 20 is the least common multiple between 4 and 10. If we list the multiples for each number, we would find that the first number they have in common is 20. The list of multiples for the number 4 is 4, 8, 12, 16, 20, 24, etc. The list of multiples for the number 10 is 10, 20, 30, etc.

A typical word problem that you might encounter that involves the least common multiple may sound like this one:

'Mike buys this particular candy that breaks into 6 pieces, and Jenny buys another type of candy where each bag contains 15 candies. What is the least number of candies that both can split between the same number of people?'

In this word problem, the least number of candies equals the number of people to be shared with, and also equals the least common multiple. So, we can find our answer by listing our multiples and then finding the first number that they have in common. Mike can split his candies between first 6 people, then 12 people, then 18, 24, 30, and so on. Jenny can share her candies with 15 people at first, then 30, then 45, and so on. What is the first number they have in common? 30. So, 30 is our answer.

Let's review what we've learned now:

- The
**greatest common factor**is the greatest factor that can be shared between two or more numbers. To find the greatest common factor, we first list all the factors of each number. Then, we find the greatest factor that is common to all the numbers. - The
**least common multiple**is the smallest multiple shared between two numbers. To find the least common multiple, we list the multiples of each number, and then look for the first number that they have in common.

Once you are done with this lesson, you should be able to:

- Identify a greatest common factor or least common multiple word problem
- Recall how to find the greatest common factor and the least common multiple of a set of numbers

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
9 in chapter 4 of the course:

Back To Course

6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- Converting Numbers to Scientific Notation 5:19
- Comparing Numbers Written in Scientific Notation 5:15
- Identifying Prime & Composite Numbers 5:07
- How to Find the Prime Factorization of a Number 5:36
- Finding the Prime Factorization with Exponents 4:44
- How to Find the Greatest Common Factor 4:56
- How to Find the Least Common Multiple 5:37
- Using Prime Factorizations to Find the Least Common Multiples 7:28
- Word Problems: Greatest Common Factor & Least Common Multiple 4:34
- Go to 6th-8th Grade Math: Number Theory

- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Computer Science 203: Defensive Security
- Black History Month Lesson Plans & Resources
- Early Childhood Lesson Plan Templates & Examples
- JavaScript Language Basics
- Forms & JavaScript
- JavaScript & HTML
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP
- MEGA Exam Registration Information
- MEGA & MoGEA Prep Product Comparison
- PERT Prep Product Comparison

- Teaching Decoding Reading Strategies
- Economic Factors Impacting Economic Development
- Using Text Structure While Reading
- What is Military Time? - Definition & Format
- Practical Application for C Programming: Data Types & Variables
- Behavioral Model for Software Requirements: Definition & Example
- Major Ocean Current Circulation: Features & Patterns
- Quiz & Worksheet - The Minister's Black Veil Analysis
- Quiz & Worksheet - Similar Polygon Practice
- Quiz & Worksheet - Using Movement to Teach Children
- Quiz & Worksheet - Dallas Winston in the Outsiders
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Classroom Management Resources for Teachers | Study.com
- ESL Games for the Classroom

- ILTS Science - Physics (116): Test Practice and Study Guide
- Accuplacer ESL Language Use Test: Practice & Study Guide
- Accounting 101: Financial Accounting
- Business 100: Intro to Business
- Psychology 104: Social Psychology
- Fifteenth-Century Italian Art
- MTEL History: Judaism
- Quiz & Worksheet - Power of a Quotient Property
- Quiz & Worksheet - Ambition Quotes in Julius Caesar
- Quiz & Worksheet - Emotional Appeals in Composition
- Quiz & Worksheet - Methods to Find the Surface Area of a Cylinder
- Quiz & Worksheet - Influence of Religion on UK's Public Life

- Dimeter: Definition & Examples
- Asian Elephant Facts: Lesson for Kids
- How to Study for a Science Test
- Sounds Experiments Lesson for Kids
- How to Ace Your Job Interview
- DNA Experiments for Kids
- Earth Science Projects
- How to Study for SAT Subject Tests
- How to Use the GED Math Prep Course
- What's in Common Core Standards Appendix C?
- Cell Project Ideas
- How Many Questions are on the TABE Test?

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject