How to identify GCF vs LCM in problem solving questions

📚 Quick Study Guide

• 🔢 GCF (Greatest Common Factor): The largest number that divides evenly into two or more numbers. Think 'Greatest' = largest factor they SHARE.
• ✨ LCM (Least Common Multiple): The smallest number that is a multiple of two or more numbers. Think 'Least' = smallest multiple they BOTH have.
• 🔎 GCF Keywords: 'Greatest', 'largest', 'maximum', 'dividing into groups', 'splitting'. These imply finding the biggest group size or the largest piece.
• 🌱 LCM Keywords: 'Least', 'smallest', 'minimum', 'repeating events', 'cycles', 'together again'. These imply finding when things coincide or repeat.
• ➗ GCF Example: Find the greatest number that divides both 12 and 18. The GCF is 6.
• ➕ LCM Example: Find the smallest number that is a multiple of both 4 and 6. The LCM is 12.
• 💡 Tip: If the problem involves dividing something into smaller groups, it's likely a GCF problem. If it involves finding when events repeat or occur together, it's likely an LCM problem.

Practice Quiz

1. What are you trying to find when a word problem asks you to cut two different lengths of ribbon into the longest possible equal pieces?
   1. GCF
   2. LCM
   3. Average
   4. Median
2. A baker has 36 chocolate cookies and 24 sugar cookies. He wants to make identical treat bags using all of the cookies. What is the greatest number of treat bags he can make?
   1. 72
   2. 6
   3. 12
   4. 36
3. Two neon signs are turned on at the same time. One sign blinks every 4 seconds and the other sign blinks every 6 seconds. In how many seconds will they blink together again?
   1. 2
   2. 10
   3. 12
   4. 24
4. What are you trying to find when a word problem asks you to determine when two buses on different routes will arrive at the same stop at the same time?
   1. GCF
   2. LCM
   3. Range
   4. Mode
5. Sarah wants to create identical bouquets of flowers using 18 roses and 27 tulips. What is the maximum number of bouquets she can make if she uses all the flowers?
   1. 9
   2. 45
   3. 3
   4. 6
6. John exercises every 3 days, and Mary exercises every 5 days. If they both exercised today, in how many days will they next exercise together?
   1. 2
   2. 8
   3. 15
   4. 30
7. A store wants to package 48 chocolate bars and 36 candy bars into identical boxes. What is the greatest number of boxes they can make?
   1. 12
   2. 84
   3. 4
   4. 6