What is the GCF and LCM of 36 and 45? | Socratic
Middle School Math Rules - Ratio, Rate, and Proportion and Measures of Central Tendency [*Make own LCM & GCF Chart linked to lots of great anchor charts. How to Use the Ladder Method to Find the Greatest Common Factor The lowest common multiple (LCM) is the smallest multiple two (or. Today we'll look at an easy method for finding the greatest common factor and least common multiple of two or more numbers. To find the GCF.
Pretty much every whole number or every integer has the common factor of 1. They both share the common factor 2 and they both share the common factor 4. So we're not just interested in finding a common factor, we're interested in finding the greatest common factor. So all the common factors are 1, 2 and 4.
Using the Ladder Method in Math - Minds in Bloom
And what's the greatest of them? Well, that's pretty easy. So the greatest common factor of 12 and 8 is 4. Let me write that down just for emphasis. Greatest common factor of 12 and 8 equals 4. And of course, we could have just as easily had said, the greatest common divisor of 12 and 8 equals 4.
Sometimes it does things a little funny. Let's do another problem. What is the greatest common divisor of 25 and 20? Well, let's do it the same way.
The factors of 25? It's actually 5 times 5. It's interesting that this only has 3 factors. I'll leave you to think about why this number only has 3 factors and other numbers tend to have an even number of factors.
Can You Find the Relationship?
And then now we do the factors of Factors of 20 are 1, 2, 4, 5, 10, and And if we just look at this by inspection we see, well, they both share 1, but that's nothing special. But they both have the common factor of? You got it-- 5. So the greatest common divisor or greatest common factor of 25 and well, that equals 5. What is the greatest common factor of 5 and 12? Well, factors of 5? That's because it's a prime number. It has no factors other than 1 and itself.
Then the factors of 12? It's 1, 2, 3, 4, 6, and So it really looks like only common factor they share is 1. So that was, I guess, in some ways kind of disappointing. So the greatest common factor of 5 and 12 is 1. And I'll throw out some terminology here for you.
When two numbers have a greatest common factor of only 1, they're called relatively prime. And that kind of makes sense because a prime number is something that only has 1 and itself as a factor. And two relatively prime numbers are numbers that only have 1 as their greatest common factor. Hope I didn't confuse you. 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.
Ask a few students to work out their examples on the board or document camera. As students give examples of different ways they can find the LCM, have the other students write the examples in their math notebook.
Ask student volunteers to explain their reasoning. Students need to see all 4 examples worked out and explained.
If I only use the prime numbers from the largest original number and only add prime numbers from the smaller original number that are not already listed, I have all of the prime numbers or basic building blocks for both 12 or I am making a multiple both 12 and 32 can make when I multiply the prime numbers for 32 and any missing prime number or building block needed to make I have broken down each number and put it back together only using the basic building blocks needed to make either 32 or Again, depending on your class dynamics, this time I would have the teacher work out the GCF using the factor tree, cake method, list method, and the Venn on the document camera instead of using student volunteers.
Ask students to justify why these methods work in finding the LCM for 49 and 84 as you work out that specific method.
We are looking for the smallest multiple 49 and 84 can make. The Venn Diagram link for example organizes both of the numbers' factors, putting each list of prime factors inside separate circles that overlap. The overlapping section contains only the prime factor that is common to both. Play a few LCM online games. This can be used during whole group or as a center. End of day one.
- Using the Ladder Method in Math
- Greatest common factor explained
- What is the GCF and LCM of 36 and 45?
Have students vote on the best one for each mathematical term. Play the video clip with the father of the bride is getting frustrated because hotdogs are packaged in quantities of 8 and hotdog buns are packaged in quantities of Ask students if they have ever had a similar situation of trying to purchase items with different quantities.
Display word problem document and work it out with the students. What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Hot dog buns come in packages of If I want to buy enough buns and dogs and have none left over, how many packages of hot dogs and hot dog buns should she purchase? Have one person from each pair get a word problemposter rubricscissors ,glueposter paper, and markers. Have sets of these supplies prepared before class, including one word problem. Cut the individual word problems from the word problems examples supplied. Remind students to use their examples from their math notebooks.
Finding the GCF & LCM of 3 or More Numbers using the Cake Method
How will the teacher assist students in organizing the knowledge gained in the lesson? Each pair will have minutes to present their poster. Students can be given the first 10 minutes of each class to finish up presentations.
An alternative approach could be to have students make a video of their presentation or create power points instead of posters. The teacher could choose 2 or 3 to show the whole class. Students could, also, simply display their posters and have students choose 2 or 3 for whole class presentation.
Summative Assessment The rubric will be used to assess students' posters that illustrate their understanding of Greatest Common Factor and Least Common Multiple. Ask students to independently answer the following two questions: What is the Greatest Common Factor for the two numbers 15, 21? Please refer to the guided questions section.