Real-World Examples of LCM: How We Use It Every Day

📚 Quick Study Guide

🔢 The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that is divisible by all the numbers. 💡 To find the LCM, you can use prime factorization or list multiples. ➗ Prime Factorization Method: Break down each number into its prime factors and then multiply the highest power of each prime factor. 📝 Listing Multiples Method: List multiples of each number until you find a common multiple. ➕ The LCM is useful for solving problems involving fractions, ratios, and periodic events. ⏰ Knowing LCM can help manage time and resources effectively.

🧪 Practice Quiz

1. What is the LCM of 4 and 6?
1. 8
2. 12
3. 18
4. 24
2. Sarah exercises every 3 days and John every 4 days. If they both exercised today, in how many days will they next exercise together?
1. 6 days
2. 7 days
3. 12 days
4. 24 days
3. A baker wants to divide 24 chocolate cookies and 36 peanut butter cookies into identical boxes. What is the maximum number of boxes he can make using all of the cookies? (Hint: Think Greatest Common Factor (GCF) for boxes, not LCM for cookies)
1. 6
2. 12
3. 24
4. 36
4. Two neon signs flash at different rates. One flashes every 6 seconds and the other flashes every 8 seconds. If they flash together now, how many seconds will pass before they flash together again?
1. 12 seconds
2. 14 seconds
3. 24 seconds
4. 48 seconds
5. What is the LCM of 5, 10, and 15?
1. 15
2. 20
3. 30
4. 50
6. You want to arrange 16 red marbles and 24 blue marbles into rows such that each row has the same number of marbles of each color. What is the largest number of marbles that each row can have? (Again, consider GCF).
1. 4
2. 6
3. 8
4. 12
7. A store receives shipments of paper plates every 18 days and plastic cups every 24 days. If they received both shipments today, how many days will it be before they receive both shipments on the same day again?
1. 30 days
2. 36 days
3. 72 days
4. 432 days