Real-World Examples of Least Common Multiple (Listing Method)

📚 Quick Study Guide

• 🔢 Definition: The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that is divisible by each of the numbers.
• 📝 Listing Method: List the multiples of each number until you find a common multiple. The smallest common multiple is the LCM.
• ➕ Example: Find the LCM of 4 and 6.
  • Multiples of 4: 4, 8, 12, 16, 20, 24,...
  • Multiples of 6: 6, 12, 18, 24, 30,...
  • LCM(4, 6) = 12
• 💡 Tip: Always start by listing multiples of the largest number first. It can sometimes speed up the process!

🧪 Practice Quiz

1. What is the LCM of 3 and 5 using the listing method?
   1. 10
   2. 15
   3. 8
   4. 30
2. Sarah goes to the gym every 3 days, and John goes every 4 days. If they both go to the gym today, in how many days will they next go to the gym together? This involves finding the LCM of 3 and 4.
   1. 6 days
   2. 12 days
   3. 7 days
   4. 24 days
3. Find the LCM of 2, 3, and 4.
   1. 6
   2. 12
   3. 24
   4. 8
4. A baker wants to divide 20 cookies and 30 brownies into identical packages. What is the largest number of packages he can make such that each package has the same number of cookies and the same number of brownies? (Hint: This requires finding a GCF first, not LCM directly, but consider how understanding multiples helps with factors! Think factors of 20 and 30).
   1. 5
   2. 10
   3. 60
   4. 2
5. What is the LCM of 7 and 8?
   1. 15
   2. 56
   3. 1
   4. 64
6. Two neon signs flash. One flashes every 6 seconds, and the other flashes every 8 seconds. If they flash together now, in how many seconds will they next flash together? (Find the LCM of 6 and 8).
   1. 14
   2. 24
   3. 48
   4. 2
7. What is the LCM of 5, 10, and 15?
   1. 5
   2. 15
   3. 30
   4. 50