Chapter 5                                                            Name:  ______________________ 
               LCM & GCF  
               Word Problems II                                                     Period:  _____ Date:  __________ 
                
                
               One of the challenges in using LCM and GCF to solve problems is identifying when 
               to use which strategy.  Here are some tips. 
                
               What is the question asking us?  
                
                        Do we have to split things into smaller sections?  
                        Are we trying to figure out how many people we can invite?  
                        Are we trying to arrange something into rows or groups?  
                                                                                     
                    If so, it is a GCF problem.   
                
                        Do we have an event that is or 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?  
                
                    If so, it is a LCM problem.   
                
               On a separate piece of paper, state whether it is a GCF or LCM problem, solve it, 
               AND show or explain how you arrived at your solution.  
                
               1)        One trip around a running track is 440 yards.  One jogger can complete one lap in 8 
                         minutes, the other can complete it in 6 minutes.  How long will it take for both joggers 
                         to arrive at their starting point together if they start at the same time and maintain their 
                         jogging pace?  
                
                
               2)        There are fewer than 6 dozen eggs in a large basket.  If you count them 2, 3, 4, or 5 at 
                         a time, there are none left over.  How many eggs are in the basket? 
                
                
               3)        Three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the 
                         same length. What is the greatest possible length of each plank ?  
                
                
               4)        Brenda and Trent are friends. Brenda is 24. The LCM of their age is 120 and the GCF of 
                         their age is 8. How old is Trent? 
                
                          
               5)        Rebecca has 20 table tennis balls and 16 table tennis paddles.  She wants to sell 
                         packages of balls and paddles bundled together.  What is the greatest number of 
                         packages she can sell with no leftover balls or paddles? 
                
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           Chapter 5                                          Name:  ______________________ 
           LCM & GCF  
           Word Problems II                                   Period:  _____ Date:  __________ 
            
            
           6)      Sara Pappas and Harry Kinnan both work the 3:00 pm to 11:00 pm shift. Sara has 
                   every fifth night off and Harry has every sixth night off. If they both have tonight off, 
                   how many days will pass before they have the same night off again? 
            
            
           7)      A choir director at your school wants to divide the choir into smaller groups. There are 
                   24 sopranos, 60 altos, and 36 tenors. Each group will have the same number of each 
                   type of voice.  
            
                   A. What is the greatest number of groups that can be formed?  
                   B. How many sopranos, altos and tenors will be in each group?  
                    
            
           8)      The GCF of two numbers is 30. The LCM is 420. One of the numbers is 210. What is the 
                   other number? 
            
            
           9)     Find the largest number which can divide 290, 460 and 552 leaving the remainders 4, 5 
                  and 6 respectively.  
            
            
           10)     There are 100 senators and 435 representatives in the United States Congress.  How 
                   many identical groups could be formed from all the senators and representatives? 
            
            
           11)     Find the greatest number of four digits which is exactly divisible by each of 12, 18, 40 
                   and 45. 
            
            
           Challenge 
            
           12)     Find the least number of square tiles required to pave the ceiling of a room 15 m 17 cm 
                   long and 9 m 2 cm wide.  
            
            
           13)     You want to make two garden plots next to each other with a fence completely around 
                   each one.  One plot is 180 square feet and the other is 204 square feet.  If the fence 
                   comes in 1 foot lengths, what is the greatest length of the fence you can make that is 
                   shared by both garden plots?  How much fencing is required? 
            
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