Greatest Common Factor and Least Common Multiple How

Greatest Common Factor and Least Common Multiple How do you find them?

WARM-UP �If you did not finish your quiz, you have 15 minutes to finish. Everyone else must remain silent. �At the beginning of the summer, Lauren had a balance $25 in her bank account. She saved a total of $145 from her summer job, which she deposited into her account. Today Lauren withdrew enough money from her account to cover her $20 athletic facilities fee and her $30 uniform fee. If Lauren made no other withdrawals or deposits, what is her account balance? The balance of Lauren’s account is $120.

What is a factor? rger la a t e g to r e th e g to ly ip lt The numbers you mu number 2 and 3 are both factors of 6. What are the other factors of 6?

What is a prime number? �Numbers that have no other factors but itself and one! �What are the first 6 prime numbers? 2, 3, 5, 7, 11, 13

What is prime factorization? �The prime numbers that multiply together to get the original number. Use the ladder method! Begin with the lowest prime number and see if it is divisible by the original number. 2. Continue until it is no longer divisible by that number, then move on to the next prime number 3. Continue dividing by prime numbers until the only number left inside the ladder is one 1.

�What is the prime factorization of 24? 2 24 2 12 2 6 3 3 Prime Factorization of 24: 2 • 2 • 3 1

�What is the prime factorization of 39? 3 39 13 13 1 Prime Factorization of 39: 3 • 13

Prime Factorization Practice �What are the first 6 prime numbers? � 2, 3, 5, 7, 11, 13 �What is the prime factorization of 32? � 2 2 2 �What is the prime factorization of 18? � 2 3 3

What is the Greatest Common Factor? �It is the largest of the common factors between two numbers. �A common factor is a factor that two numbers have that are the same https: //www. flocabulary. com/gcf-lcm/

How do I find common factors? �What are all the common factors of 10 and 20? �What numbers multiply together to make 10? � 1 and 10; 2 and 5 �What numbers multiply together to make 20? � 1 and 20; 2 and 10; 4 and 5 �What are all the factors that the numbers shared (common factors)? � 1, 2, 5, 10 � What is their greatest common factor? � 10

Method 1: Venn Diagram �What are the common factors of 12 and 16? 1 12 2 6 3 4 Factors of 12 The common factors of 12 and 16 1 1 16 2 2 8 4 4 Factors of 16 The GCF is the largest of the common factors which is 4!

Method 2: Rainbow! �What is the greatest common factor of 16 and 36? � 16: 1, 2, 4, 8, 16 � 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 The greatest common factor or 16 and 36 is 4. List all the factors of each of the numbers. Once you either have 2 of the same factors or numbers that are so close there are no other factors between them, then you’ve reached the middle of the rainbow.

Rainbow Method Again �What is the greatest common factor (GCF) of 48 and 24?

Method 3: Find each number’s prime factorization �What is the greatest common factor of 12 and 18? 2 12 2 6 33 2 18 3 9 What do 3 3 they have in 1 common? 1 2 • 3=6 2 • 3 The greatest common factor of 12 and 18 is 6.

Prime Factorization Method AGAIN!! �What is the greatest common factor (GCF) of 14 and 28?

What is the greatest common factor of 28 and 35? �Use both methods � 28: 1, 2, 4, 7, 14, 28 � 35: 1, 5, 7, 35 2 28 2 14 77 1 2 • 7 Using the rainbow method, the GCF is 7. 5 35 7 7 1 5 • 7 Using the prime factorization method, the GCF is 7.

Warm-Up 1. What is the prime factorization of 48? Prime Factorization of 24: 2 • 2 • 2 3 2. What is the GCF of 35, 21, and 84? The GCF of 35, 21, and 84 is 7.

What is a multiple? �The number you get when you multiply a number by another number What are the multiples of 5? 5, 10, 15, 20, 25, 30…

What is the least common multiple? �It is the smallest multiple that is shared between two numbers.

How to find LCM It’s simple…Just list the multiples of each number until you find one that is in common! What is the LCM of 4 and 7? 4: 4, 8, 12, 16, 20, 24, 28 7: 7, 14, 21, 28

What is the LCM of 12 and 16? 12: 12, 24, 36, 48 16: 16, 32, 48

Which should you use to solve the problem, GCF or LCM? �Two shuttles leave the Hard Rock Hotel to go to Universal Studios at the same time. The Minion Madness shuttle returns to the hotel every 8 minutes. The Incredible Hulk shuttle returns to the hotel every 10 minutes. In how many minutes will Minion Madness and the Incredible Hulk leave the hotel together for the second time? Use the LCM! The shuttles will leave the hotel at the same time in 40 minutes.

Which should you use to solve the problem, GCF or LCM? �Mr. Schuester directs two show choirs. One choir has 28 students. The other choir has 36 students. For rehearsals, he wants to divide each chorus into the largest possible equal groups with no students left over. How many students will be in each group? Use the GCF! Mr. Schuester can divide each choir into groups of 4.

Warm-Up 1. Find the GCF of 28 and 42 using prime factorization(ladder method). 28 = 2 2 7 and 42 = 2 3 7 The GCF of 28 and 42 is 14. 2. What is the LCM of 12 and 32? The LCM of 12 and 32 is 96.

Warm-Up �What is the greatest common factor (GCF) of 32 and 72? The GCF of 32 and 72 is 8. �What is the least common multiple of 6 and 4? The LCM of 6 and 4 is 12.

Distributive Property!!! üLet’s have Tim and Moby gives us the basics. : ) http: //www. brainpop. com/math/numbersandoperations/distri butiveproperty/

How does the distributive property work? The number outside the parentheses “jumps” over the parentheses and multiplies by each number inside! Just bring down the sign! Multiply and then add! 2(2 + 3) (2 • 2) + (2 • 3) (4) + (6) =10

You can write a number or sum in distributive form… �How can you write an expression equal to 33 + 77 using distributive form? 1. Find the GCF of the two numbers. (This will go outside of the parentheses. ) � GCF: 11 � 11() 2. Now use the other factor that multiplies with the GCF to get the original number. (Those 2 numbers go inside of the parentheses. ) � 3 • 11 & 7 • 11 � 11(3 + 7)

Now you try some! �Rewrite the following expressions using the distributive property. �Remember, find the GCF first! � 100 + 8 � 4(25 + 2) � 25 + 10 � 5(5 + 2) � 24 + 14 � 2(12 + 7) � 63 + 21 � 21(3 + 1)