Chapter 3
Section 3.1 LCMGCF
multiples Multiples of 4 4,8,12,16,20… Multiples of 10 10,20,30,40,50… Multiples are larger than the original number
LCM Least Common Multiple Can be calculated for 2 or more numbers Remember: Multiples are larger than the original number LCM asks for the smallest multiple that the numbers in question have in common
Method 1 & 2 Method 1: List out the multiples Ex: Find the LCM of 7 and 5 7, 14,21,28,35,42,49, 56, 63, 70, 77 5, 10,15,20,25,30,35,40, 45,50,55,60,65,70, 75 Ex2: Find the LCM of 8 and 12 24 Try it: Find the LCM of 8 & 18
Method 2 Prime Factorization Prime Factor each number Choose the largest amount of each number that they have in common Multiply with the numbers each do not have in common You have your LCM EX: LCM of 120 and 36 120 = 2 3* 3*5 36 = 2 2 *3 2 LCM = 2 3* 3 2* 5 = 8*9*5=360 Ex2: LCM of 12 & 4 12 = 2 2 *3 4 = 2 2 LCM = 2 2 *3 = 4 * 3 = 12 Try it: Find the LCM of 12, 18, & 40
GCF Greatest Common Factor Factors are smaller!!! GCF = Greatest of the factors that the numbers have in common
Method 1 List out the Factors of the numbers Ex1: 18 & 20 18 = 1,2,3,6,9,18 20 = 1,2,4,5,10, 20 GCF = 2 Try it: Find the GCF of 25 & 52
Method 2 Prime Factorization Method Same as LCM prime factoring except select the smallest amount of each and ignore the numbers they do not have in common. Ex: 16 & 20 16 = 2 4 20 = 2 2 *5 GCF = 2 2 = 4 Try it: Find the GCF of 32,40,56 GCF = 8
U TRY IT Find the LCM of : 3 & 9 3, 12, 18 Find the GCF of: 12 & 54 24 & 36 & 60 You go to the bulk section of your online grocery store to buy bulk dvd-R’s. The deal is that you must order 20, 50 or 100. What size packages should the store keep in their warehouse so they never have to open a package because of an order by some customer? GCF 10
HW 3.1 1 – 56 eoo Problems 57 – 64 all except 60 & 61 Evens: 2, 6, 12, 18, 20, 24, 24, 26, 38, 44, 48, 50, 54, 56 Try to do the easy ones in your head