Amy has a master's degree in secondary education and has taught math at a public charter high school.
Greatest Common Factor
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.
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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.
Least Common Multiple
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
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Word Problems: Greatest Common Factor & Least Common Multiple
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