Word Problems Involving Greatest Common Factor and Least Common Multiple

Name ______Date ______

GCF and LCM Word Problems

Solve each word problem by finding GCF or LCM. 5. Two neon lights are turned on at the same 1. Pencils come in packages of 10. Erasers time. One blinks every 32 seconds and the come in packages of 12. Phillip wants to other blinks every 48 seconds. When will purchase the smallest number of pencils they blink at the same time? and erasers for the school year. How many packages of pencils and erasers should Phillip buy? a) Smallest number of pencils and erasers? ____ b) How many packages of pencils total? ______6. The table below shows the number of c) How many packages of erasers total? _____ students in the school choir.

School Choir (Use for Question 6) Students Number 2. Kiara baked 30 oatmeal cookies and 48 Girls 48 chocolate chip cookies to package in plastic Boys 64 containers for her friends at school. If she wants each container to have the greatest number of cookies possible, how many The choir teacher plans to arrange the plastic containers does she need? students in equal rows. Only girls or boys a) How many plastic containers? _____ will be in each row. What is the greatest b) How many oatmeal cookies? ____ number of students that could be in each c) How many chocolate chip cookies? _____ row? ______# rows of boys? _____ #rows of girls? ______

3. Boxes that are 18 inches tall are being stacked next to boxes that are 24 inches tall. What is the shortest height at which the two stacks will be the same height? Items in the Gift Bags (Use for Question 7) Items Bags T-shirt Every 10th visitor Backpack Every 14th visitor

4. Beginning at 8:30 A.M., tours of the 7. At a display booth at an amusement park, National Capitol and the White House every visitor gets a gift bag. Some of the begin at a tour agency. Tours for the bags have items in them as shown in the National Capitol leave every 15 minutes. table above. What lucky visitor will be the Tours for the White House leave every 20 first to get the both (same) the t-shirt and minutes. How often do the tours leave at backpack in their bag? the same time?