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, would you want to find the LCM (least common multiple) or GCF (greatest common factor)? Explain your answer.
LCM (explain your answer for full credit)
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
What is the greatest common factor of 5 and 10? (show all your work to justify your answer!)
gcf is 5
Martha wants to buy packs of cupcakes for a party. Chocolate cupcakes come in packs of 6, and Strawberry cupcakes come in packs of 8.
If Martha wants to buy enough cupcakes so that she has the smallest equal number of chocolate and strawberry cupcakes, should she find the GCF or the LCM? Explain your answer.
LCM (explain your answer for credit)
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 (15,9)
Show all the steps you did to justify your answer.
LCM (15,9) = 45
Find the LCM (7,6)
Show all the steps you did to justify your answer.
LCM(7,6) = 42
What is the GCF of 210 and 12? Justify your answer by explaining or showing your work.
GCF is 6
What is the GCF of 28 and 40? Justify your answer by explaining or showing your work.
GCF is 4
Samantha and Karl both rented movies today. Samantha rents a movie every 11 days. Karl rents a movie every 3 days. How many days until they rent movies on the same day again? Show all your work to justify your answer.
They will rent movies on the same day again in 33 days.
Find the LCM of 7, 21, and 35
105
Find the LCM of 32 and 28.
Show all your work to justify your answers.
LCM is 224
The GCF of 45, 10, and _____ is 5. The missing number is not 5.
What is the missing number? Show your work or explain you know your answer is correct.
(There are many possible answers, write your answer and explain / show your work to justify it!)
The GCF of 27, 9, and _____ is 3. The missing number is not equal to 3.
What is the missing number? Show your work or explain you know your answer is correct.
(There are many possible answers, write your answer and explain / show your work to justify it!)
In October, Kristin has ballet rehearsal every 2 days, and she has track meets every 7 days. How many times will she 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.
There will be 14 days until they overlap again each time.