# Common Multiples

Warmup

Activity #1

`Discover Common Multiples. ` Lin’s uncle is opening a bakery. On the bakery’s grand opening day, he plans to give away prizes to the first 50 customers that enter the shop. Every fifth customer will get a free bagel. Every ninth customer will get a free blueberry muffin. Every 12th customer will get a free slice of carrot cake.

(1.) Diego is waiting in line and is the 23rd customer. He thinks that he should get farther back in line in order to get a prize. Is he right?

(2.) If so, how far back should he go to get at least one prize? Explain your reasoning.

(3.) Jada is the 36th customer. Will she get a prize? If so, what prize will she get?

(4.) Is it possible for Jada to get more than one prize?

(5.) How do you know? Explain your reasoning.

(6.) How many prizes total will Lin’s uncle give away? Explain your reasoning.

Activity #2

Finding Common Multiples by Modelling. • Drag the red points on the figures to the right end. 60 is a common multiple.​
• Note the number of parts that divide each rectangle.​
• Are there any lines that are in matching positions?​
• Can you guess the number on that line?​
• Would you say the number you guessed above is another common multiple of 6 and 10?​
• Enter two different numbers (not greater than 20) and drag the red points to find their common multiples. ​
• To increase 3 numbers, check the upper box.

Activity #3

Finding Least Common Multiple. (1.) The least common multiple of 6 and 8 is 24. What do you think the term “least common multiple” means?

(2.) Find all of the multiples of 10 and 8 that are less than 100. Find the least common multiple of 10 and 8.

(3.) Find all of the multiples of 7 and 9 that are less than 100. Find the least common multiple of 7 and 9.

(4.) What is the least common multiple of 10 and 20?

(5.) What is the least common multiple of 4 and 24?

(6.) In the previous two questions, one number is a multiple of the other. What do you notice about their least common multiple?

(7.) Do you think this will always happen when one number is a multiple of the other? Explain your reasoning.

Challenge #1

(1.) A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time?

(2.) A red light blinks every 12 seconds and a blue light blinks every 9 seconds. When will both lights blink at the same time?

(3.) Explain how to determine when 2 lights blink together.

Challenge #2

(1.) List all multiples of 10 up to 100.

(2.) List all multiples of 15 up to 100.

(3.) What is the least common multiple of 10 and 15?

Challenge #3

Cups are sold in packages of 8. Napkins are sold in packages of 12. What is the fewest number of packages of cups and the fewest number of packages of napkins that can be purchased so there will be the same number of cups as napkins?

Quiz Time