Least Common Multiple
List the first five multiples of 12.
12, 24, 36, 48, 60, ...
List the first five multiples of 18
18, 36, 54, 72, 90, ...
List all the factors of 80.
1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.
List the factors of 32
1, 2, 4, 8, 16, 32
In music class, we practice a specific rhythm. The class claps every 4 beats and they stomp their feet every 3 beats.
If you wanted to figure out how many beats it takes for them to clap and stomp their feet at the same time again, would you want to find the LCM (least common multiple) or GCF (greatest common factor)? Explain your answer.
Use that to find how much time (how many beats) it takes for them to stomp and clap at the same time.
LCM (explain your answer for full credit)
12 beats (show your work)
Given the following multiples, what is the Least Common Multiple of 7 and 3?
multiples of 7: 7, 14, 21, 28, 35, 42, ...
multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...
LCM of 7 and 3 is is 21
What is the least common multiple of 5 and 10?
multiples of 5: 5, 10, 15, 20, 25, ...
multiples of 10: 10, 20, 30, 40, ...
The least common multiple is 10
What is the greatest common factor of 75 and 12?
factors of 75: 1, 75, 3, 25, 5, 15
factors of 12: 1, 12, 2, 6, 3, 4
GCF of 75 and 12 is 3
What is the greatest common factor of 5 and 10? (show all your work to justify your answer!)
gcf is 5
Martha baked 54 chocolate cupcakes and 18 strawberry cupcakes to sell in smaller packages
She wants to split them into identical packages with the combination of cupcakes, with no left overs or split cupcakes. What is the largest number of identical packages can she make?
To show your work, choose the LCM or GCF Strategy. Then show all your work to solve for the answer.
GCF
18 packages
Find the LCM (7, 4)
1. List out the first seven multiples of 7 and 4.
2. Circle the multiples that are the same in both lists.
3. Write down the LEAST common multiple
The least common multiple (LCM) of 7 and 4 is 28
Find the LCM of 12 and 10
1. List out the first six multiples of 12 and 10.
2. Circle the multiples that are the same in both lists.
3. Write down the least common multiple
The LCM of 12 and 10 is 60
What is the greatest common factor of 21 and 9? Justify your answer by explaining or showing your work.
GCF of 21 and 9 is 3.
What is the greatest common factor of 36 and 50?
Greatest common factor is 2.
Marvin visits his friends every 3 days. He visits his cousin every 8 days. He visited his friends and his cousin today. How many days until Marvin visits both his friends and his cousin again on the same day? Show all your work to justify your answer.
It will be 24 days until Marvin visits both his friends and cousin again on the same day.
Find the LCM of 15 and 9
Show all the steps you did to justify your answer.
LCM (15,9) = 45
Find the LCM of 6 and 7
Show all the steps you did to justify your answer.
LCM(7,6) = 42
Find the GCF of 24 and 36.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 9, 12, 18, 36
The GCF of 24 and 36 is 12.
What is the GCF of 28 and 40? Justify your answer by explaining or showing your work.
GCF is 4
The soccer team has both 7th and 8th graders. There are 6 seventh graders and 10 eighth graders on the team. For a drill, the coach wants to split them into the most amount of groups while still having the same mix of seventh and eighth graders. How many groups can he have?
Show all your work to justify your answer.
2 groups.
Find the LCM of 7, 21, and 6
42
Find the LCM of 30, 15, and 9.
Show all your work to justify your answers.
LCM is 90
Find the GCF of 45, 10, and 20. Show all your work to prove your answer.
GCF is 5.
Find the GCF of 27, 9, and 3. Show all your work to prove your answer.
GCF is 3.
In October, Kristin has ballet rehearsal every 2 days, and she has track meets every 7 days. How many times will her track meets and ballet rehearsals overlap in October? How many days will there be until they overlap again each time?
(note: Oct has 31 days total)
They will overlap 2 times in October.
There will be 14 days until they overlap again each time.