How are GCF and LCM alike? | Socratic
Example: Find the greatest common factor of 24 and 30, GCF(24,30) of the two circles on the Venn diagram. Least Common Multiple in Venn Diagrams. Example: Find the greatest common factor of 24 and 30, GCF(24,30) of the two circles on the Venn diagram. Least Common Multiple in Venn Diagrams. Using Venn diagrams. A Venn diagram shows the relationship between different sets or categories of data. Find the HCF and LCM of 12 and Break the.
What are the guiding questions for this lesson? How did you redefine GCF? Find the biggest number that both can divided by: How might you show the factors of these numbers? How might you decide which is the biggest and is a factor of both? How can I use this definition to find the LCM of 12 and 32?
GCF and LCM with Venn Diagrams
The smallest number that is a multiple for each number: How might I show the multiples for each number? How would I find the smallest that is the same for both. If I want to have enough hotdogs and buns to serve each of 24 people exactly one hotdog and bun and have none left over, how many packages of hot dogs and hot dog buns should I purchase?
The package of hotdogs contains 8 hotdogs, and the package of buns contains 12 buns. How will the teacher present the concept or skill to students?
Have a timer with sound running as students walk in. This should be big and bold enough to catch students' attention. There needs to be space under each sign for students to post sticky notes.
Have a blank set of stickies in order of blue, yellow, and green lined up under each mathematical term. The school media center may have a class supply. You have three sticky notes for each term and a dictionary or thesaurus.
You may use more than one word or a phrase to replace each word example: We will start with the mathematical term greatest common factor. You will have 4 minutes to find another way to say greatest common factor and post it under GCF on the board. The blue sticky will represent greatest, the yellow sticky will represent common, and the green sticky will be used to represent factor. On your mark, get set, go! Use the same procedure for least common multiple. Only give the students minutes.
Now the students know what they are doing and have already redefined the word common. What activities or exercises will the students complete with teacher guidance? Review the redefined mathematical term GCF and apply this better understanding to numbers. Higher level students might choose 2 more challenging numbers. Use the timer to give students 5 minutes.
Adjust time for student ability.
All students might not have finished 2 examples. Have them think of a question that would help them become 'unstuck'. How can I find what numbers 12 and 32 are divisible by? Giving students extra points is a good incentive to ask and answer their own questions.
Ask a few students to work out their examples on the board or document camera of different ways they can find the GCF. As students work out examples on the board, have the other students write the examples in their math notebook.
Support students' organized thinking with the displays, and, if necessary, add to the strategies students display. Ask students to articulate and justify their method and reasoning. Finding the GCF means we are looking for the biggest number that both original numbers can be divided by. When I break the original number down, to where it cannot broken down any further, I have found all the prime numbers that make the original number.
Looking at the primes each original number has in common, shows all the numbers they are divisible by. When I multiply the primes they have in common, I find the greatest factor each original number is divisible by.
Depending on your class dynamics, this time I would have the teacher work out the GCF using the factor tree, cake method, and the list method on the document camera instead of using student volunteers. Have students write the examples in their math notebooks.
Ask students to justify why these methods work in finding the GCF for 49 and 84 as you work out that specific method. We are looking for the greatest common factor or the biggest number 49 and 84 are divisible by.
The list method lists all of the numbers' factors. Now you can see the biggest factor they have in common. Play a few online GCF games to practice.
This can be done whole group or as a center. Review the redefined mathematical term LCM and apply this better understanding to numbers. How can I find the smallest multiple 12 and 32 can make? Again, giving students extra points is a good incentive to ask and answer their own questions.
How to Find the LCM & GCF of a number set with a Venn diagram « Math :: WonderHowTo
Ask a few students to work out their examples on the board or document camera. Shame it's so time-consuming. And, in my experience, students sometimes miss factors from their list. One way to avoid this is by listing factors using a pairing method like this: Factor rainbows are a pretty alternative see this article from the NCTM. First, we need to do a prime factor breakdown.
Once you have the prime factors of each number, draw a Venn diagram and place the common factors in the intersection of two sets, as shown in the example below. Even though I taught the Venn method for years, I'm not a huge fan of it. In my experience, students are ok with filling in the Venn diagram but then they often can't remember which 'bit' is the HCF. If they do remember the method then they probably don't have a clue why it works. Confusingly, it seems that some people use a different Venn method which involves putting all factors not prime factors into a Venn diagram and identifying the highest factor in the intersection see example below.
This is another form of the listing method described above - it's just a different way of organising the list. Let's call this Lenn Method - it's a hybrid of Venn and Listing. Write the prime factors of each number out as shown in the example below so it's easy to see which factors appear in both number - the product of these is the HCF. This method is featured in this post by Don Steward. It sounds complicated but it's incredibly easy. Try a few examples yourself to see how straightforward it is.
The method including why it works is explained in James Tanton's video below. I really like this method but for some reason I'm hesitant to use it with students Note that this method doesn't give you the Lowest Common Multiple, but it's easily found once you've got the Highest Common Factor.
I'm not sure it's really called the Indian Method, I'm only calling it that because of this video. At my school we call it the Korean Method because a Korean student introduced it to us!
I've found that my students really like it. It's hard to go wrong. It's easy to explore why it works too. Write down the two numbers, then to the left, as in my example above write down any common factor. Now divide and by 5 and write the answers underneath 63 and 84 in this case.
Keep repeating this process until the two numbers have no common factors ie 3 and 4 above. Now, your Highest Common Factor is simply the product of numbers on the left. And for the Lowest Common Multiple, find the product of the numbers on the left and the numbers in the bottom row to find the LCM, look for the L shape.
The only difference between this and the Indian Method is that here we can only remove prime factors. This seems unnecessary - the Indian Method is quicker. In the example below, why divide by 2 if you spot larger common factors?
Resourceaholic: Tricks and Tips 1: HCF
Why not start by dividing by 4, 6 or 12? Integers I really like this set of questions from Don Steward. The following question confused one of my brightest Year 10s: To survey the number of dandelions they want to divide it equally into the minimum number of square plots.
What is the size of each square plot and how many such squares will there be? This is what she did: But she realised that her answer made no sense.
- Multiples, factors, powers and roots
- Can You Find the Relationship?
- How are GCF and LCM alike?
Can you see where she went wrong? Although you can divide 8.