Using Common Multiples and Common Factors

Warmup

Activity #1

Finding the GCF and LCM of Numbers.

• Try to find the HCF and LCM of the numbers below on a sheet of paper. The prime factorization is already done for you. ​
• Now, uncheck the boxes to see the answers. If you need help on what is done, read the highlighted information carefully.​
• Enter new numbers in the boxes and press the Enter key.​
• Repeat the steps above. Practice as much as time allows you for better understanding.

Activity #2

Finding LCM and HCF of Two Numbers.

• Move the slider to the right.​
• On a sheet of paper, find the HCF of 12 and 18.​
• On a sheet of paper, find the LCM of 12 and 18.​
• Check the boxes to verify your answers.​
• Enter new numbers to continue.​

Activity #3

Practice Questions.

• Read carefully through and answer the questions that follow.

Diego has 48 chocolate chip cookies, 64 vanilla cookies, and 100 raisin cookies for a bake sale. He wants to make bags that have all three cookie flavors and the same number of each flavor per bag.

(1.) How many bags can he make without having any cookies left over?

(2.) Find the another solution to this problem.

(3.) Find the product of 12 and 8.

(4.) Find the greatest common factor of 12 and 8.

(5.) Find the least common multiple of 12 and 8.

(6.) Find the product of the greatest common factor and the least common multiple of 12 and 8.

(7.) What do you notice about the answers to question 1 and question 4?

(8.) Choose 2 other numbers and repeat the previous steps. Do you get the same results?

Challenge #1

The school nurse is assembling first-aid kits for the teachers. She has 75 bandages and 90 throat lozenges. All the kits must have the same number of each supply, and all supplies must be used.

(1.) What is the largest number of kits the nurse can make? What kind of mathematical work was involved?

(2.) How many bandages and lozenges will be in each kit? What kind of mathematical work was involved?

Challenge #2

Mai, Clare, and Noah are making signs to advertise the school dance. It takes Mai 6 minutes to complete a sign, it takes Clare 8 minutes to complete a sign, and it takes Noah 5 minutes to complete a sign. They keep working at the same rate for a half hour.

(1.) Will Mai and Clare complete a sign at the same time? Explain your reasoning.

(2.) Will Mai and Noah complete a sign at the same time? Explain your reasoning.

(3.) Will Clare and Noah complete a sign at the same time? Explain your reasoning

(4.) Will all three students complete a sign at the same time? Explain your reasoning