1. Lesson 4.4 Least Common Multiple
Essential Question: How do you find the least common multiple (LCM) of two or more numbers?

2. Before we start…
You get an from your cousin on Wednesday. After that you receive an from your cousin every other day. When will you get an from your cousin on a Wednesday again?

3. What is a multiple?
The product of the number and any nonzero whole number.
A common multiple is a multiple that is shared by two or more numbers.

4. What is a least common multiple?
The least common multiples of two or more whole numbers.
It’s the smallest answer that two numbers share.

5. 4 has the multiples: 4, 8, 12, 16, 20, 24, 28,...
7 has the multiples: 7, 14, 21, 28, 35, 42, 49,...
The LCM of 4 and 7 would be 28.

6. How do you find a LCM? Write the prime factorization of each number.
Circle the greatest power of each prime factor.
Find the product of the circled factors. This is your LCM.

7. Find the LCM of 6 and 15.

8. Find the LCM of 16 and 24.

9. Find the LCM of 20 and 25.

10. Find the LCM of 6, 8, and 20.

11. Find the LCM of 15, 30, and 50.

12. Agriculture Crop rotation is a system in which farmers vary the crops they plant in their fields each year. Suppose a farmer grows alfalfa in a certain field every 6 years. In another field, the farmer grows alfalfa every 10 years. This year, the farmer is growing alfalfa in both fields. In how many years will the farmer grow alfalfa in both fields again?

13. Class Sizes A teacher can arrange a class into groups of 2, 5, or 6 students with no one left out. What is the least number of students that the teacher can have in class to do this?

14. Cooking Zoe is making lasagna for a family reunion
Cooking Zoe is making lasagna for a family reunion. Her recipe calls for 12 noodles of each batch of lasagna. One box of lasagna noodles contains 14 noodles. What is the least number of batches of lasagna Zoe can make without having any noodles left over?

15. How do I find the LCM of monomials?
You will use the same method to find an LCM of monomials as you did numbers.
Write the prime factorization of each number.
Circle the greatest power of each prime factor.
Find the product of the circled factors. This is your LCM.

16. Find the LCM of 6 𝑥 2 𝑦 and 9 𝑥 4 𝑧.

17. Find the LCM of 9𝑥 𝑦 2 and 15 𝑥 2 𝑦.

18. Find the LCM of 4𝑎 𝑏 2 and 10 𝑎 2 𝑏.

19. Find the LCM of 4 𝑥 3 𝑦 3 and 18𝑥 𝑦 5 .

20. What is a least common denominator?
The least common denominator (LCD) of two or more fractions is the least common multiple of the denominators.
The LCD helps us to compare fractions.

21. Orangutans A female orangutan is about 3 3 7 feet tall
Orangutans A female orangutan is about feet tall. A male is about feet tall. Which of the two orangutans is taller?

22. Walkers Sarah walks two thirds mile to school every day
Walkers Sarah walks two thirds mile to school every day. Amy walks five eighths mile to school. Who walks the greater distance to school?

23. Little League World Series Teams from California have played in the world championship game of the Little League World Series 20 times and won 5 times. Texas teams have appeared in 7 world championships and won twice. Which state has won a greater fraction of their world championship games? What is the fraction?

24. Long Jump At a track meet, your first jump is meters, your second jump is meters, and your third jump is meters. Which jump is the longest?

25. Order the numbers from least to greatest: 4 7 16 , 19 4 , 35 8

26. Order the numbers from least to greatest: 2 7 9 , 2 5 12 , 11 4

27. Order the numbers from least to greatest: 7 10 , 2 1 3 , 5 6

28. How do you find the least common multiple (LCM) of two or more numbers?

29. Ticket Out the Door
Find the least common multiple of 10 and 16.