Greatest Common Factor The class definition should be typed in here. Example: The biggest number that both numbers can be divided by. Greatest Common Factor

Word Problems that use GCF … cut things into smaller sections equally put 2 or more sets of items into the largest grouping ask how many people we can invite arrange into rows or groups Students need to look at the most efficient and systematic way to solve word problems. Word problems that entail taking amounts/things and putting it into equal groups, going from larger to smaller sections or evenly distributing people/objects will use GCF.

A GCF word Problem What questions are we trying to answer? Jenifer baked 30 brownies and 48 cookies to put into plastic containers for her friends at school. She wants to divide the brownies and cookies so that each container has the same number brownies and cookies.   What is the least amount of containers she will need?   How many brownies will be in each container? How many cookies will be in each container?

What information is needed to find the answer? Jenifer has 30 brownies and 48 cookies And wants to put them into containers that all have the same amounts of brownies and cookies GCF - we are dividing both (Common) 30 brownies and 48 cookies into equal groups(Factor) ,using the most(Greatest) amount of brownies and cookies each container We need the greatest amount in each container to use the least amount of containers possible.

Solving GCF: List 30 (1, 2, 3, 5, 6, 10, 15, 30) 48 (1, 2, 3, 4, 6, 8, 12, 16, 24, 48) Prime Factorization 48 4 2 12 3 30 15 3 5 2 Once a prime number match is found, you can not use that prime number again. I refer to the “matches” as dates and you can only take one date to the prom. The factors in common are 2x3

Now that I know the GCF… The biggest number I can divide both 30 and 48 into is 6. I will need 6 containers. How many brownies in each container? How many cookies in each container? 30 brownies put into 6 groups = 5 brownies in each 48 cookies put into 6 groups = 8 cookies in each

Use the class definition for LCM here Lowest Common Multiple

LCM Word Problems ask… events that will be repeating over and over get multiple items in order to have enough Find out when something will happen again at the same time

LCM word Problem What question are we trying to answer? Pencils come in packages of 10. Erasers come in packages of 12. Lily wants to purchase the smallest number of pencils and erasers so that she will have exactly 1 eraser per pencil. How many packages of pencils and erasers should Lily buy? What is the smallest number of pencil packs and eraser packs should Lily buy, so that she will have exactly 1 eraser per pencil ?

What information do I need to answer the question?  Pencils come in packages of 10 and erasers in packages of 12. How many packages do I need to buy of each until I have the same amount? LCM - we are trying to figure out the smallest (Least) number of pencil packs (10) and eraser packs (12) (Multiple) to have the same amount of each (Common)

Solving LCM List method 10: 10, 20, 30 , 40, 50 , 60 6 packages of 10 pencils=60 pencils 12: 12, 24, 36, 48, 60 5 packages of 12 erasers=60 erasers Prime factorization 10 ( 2 ,5) and 12 (2, 2, 3) Prime factors from the largest # 12: ( 2, 2, 3) include any prime numbers from 10: (5) 2 x 2 x 3 x 5 = 60 Using prime factors from the largest number and then including any other missing prime numbers, ensures that you are using the least amount of prime factors to make either number. (1, 2, 2, 3 and 5) are the prime factors that will give the LOWEST common multiple.

Now that I know the LCM… The smallest amount that I need, is 60 pencils and 60 erasers, to have exactly one pencil per eraser . That means I will need 6 packages of (10) pencils and 5 packages of (12) erasers .

GCF and LCM They both deal with the relationship between 2 numbers. GCF is looking for the greatest factor that numbers have in common (divide). Taking two numbers and putting them into equal groups. LCM is looking for a multiple that two or more numbers have in common (multiply). Taking the numbers and continuing a pattern until they meet.