Transcript GCF
GCF Do we want to split things into smaller sections? Are we trying to figure out how many people we can invite? Are we trying to arrange something in rows or groups? LCM Do we have an event that will be repeating over and over? Will we have to purchase or get multiple items in order to have enough? Are we trying to figure out when something will happen again at the same time? Finding the Greatest Common Factor of Two Numbers Largest factor that two or more numbers have in common The GCF of 36 and 90 1) Prime factor (factor trees) each number. Do NOT write in exponential form. 36 = 2 ● 2 ● 3 ● 3 90 = 2 ● 3 ● 3 ● 5 2) Circle each pair of common prime factors. 3) Multiply one of each common factor. 4) The product will be the Greatest Common Factor: 2 ● 3 ● 3 = 18 Finding the Least Common Multiple of Two Numbers The smallest multiple that two numbers have in common. The LCM of 12 and 15 1) Prime factor each number. 12 = 2 ● 2 ● 3 15 = 5 ● 3 2) Circle each pair of common prime factors. 3) Circle each remaining prime factor. 4) Multiply together one factor from each circle to get the Least Common Multiple : 2 ● 2 ● 3 ● 5 = 60 Any common factors are ONLY multiplied once. GCF Do we want to split things into smaller sections? Are we trying to figure out how many people we can invite? Are we trying to arrange something in rows or groups? LCM Do we have an event that will be repeating over and over? Will we have to purchase or get multiple items in order to have enough? Are we trying to figure out when something will happen again at the same time? **Underline words that could mean LCM or GCF. Use your checklist to determine whether it is a GCF or LCM problem. Bridget has swimming lessons every fifth day and diving lessons every third day. After how many days will she have both a swimming lesson and a diving lesson on the same day? GCF Do we want to split things into smaller sections? Are we trying to figure out how many people we can invite? Are we trying to arrange something in rows or groups? LCM Do we have an event that will be repeating over and over? Will we have to purchase or get multiple items in order to have enough? Are we trying to figure out when something will happen again at the same time? First, decide whether the problem is GCF or LCM. Georgine is making fruit baskets. She has 15 apples and 18 oranges. Georgine wants to make all the fruit baskets identical without having any pieces of fruit left over. What is the greatest number of fruit baskets Georgine can make?