# What is the relationship between lcm and gcf lessons

### Sixth grade Lesson Multiples, LCM, and GCF | BetterLesson

Solve word problems where you either need to find the GCF or LCM. We will learn the relationship between H.C.F. and L.C.M. of two numbers. Then we need to find the lowest common multiple (L.C.M.) of 15 and 18 which is Highest common factor and lowest common multiple of two numbers are 18 and respectively. Grade 6 - Mathematics Curriculum - Relation Between G.C.D. and L.C.M. - Math Grade appropriate lessons, quizzes & printable worksheets. The greatest common divisor (GCF) of two positive whole numbers is the product of the prime .

If something is a multiple of 10, you can skip count by tens and eventually say the number. I have students work on the practice page in pairs. Once most students have completed the practice page, we come together. I ask students what they notice about multiples of 9.

## Relationship between H.C.F. and L.C.M.

I have students think-pair-share about this question. I am looking for students to notice that if you add the digits of any multiple of 9 you get a number that is a multiple of 9. Students can prove this by dividing by 9. Students should notice a similar rule with multiples of 3. These questions have students engaging in MP 7: Look for and make use of structure and MP8: Look for and express regularity in repeated reasoning.

A common misconception is that you can always find the least common multiple by multiplying the two numbers together. I am looking for students to use 1 as a counterexample. The least common multiple is I ask students how we could write a new statement that is correct.

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.

## Multiples, LCM, and GCF

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.

### GCF & LCM word problems (practice) | Khan Academy

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.

- Can You Find the Relationship?
- What is the difference between LCM and HCF?

Play a few LCM online games. This can be used during whole group or as a center. End of day one. 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?