LCM/GCF
1.
Emily’s family just purchased two new cars. While reading the owner’s manuals, they realized that one of the cars needs an
oil change every 3000 miles. The other car needs an oil change every 4000 miles. How many miles will be on each car
when they are both taken in for an oil change together for the first time? How many miles will be on each car when it
happens again? Describe the pattern.
2.
The local diner serves fried chicken every sixth day and steak every eighth day. If fried chicken and steak are both served on
March 3rd, how many days will pass before they are both on the menu again? What will the date be?
3.
What is the largest number that divides both 70 and 105 evenly?
4.
Mrs. Knouff planning to take her friends on a hiking trip to Clifton Gorge in Yellow Springs, Ohio. She is making snack packs
for each of her friends to take on the trip. She has 24 bananas and 36 hard boiled eggs. Each snack pack will have the same
number of bananas and eggs. What is the greatest number of friends Mrs. Knouff can take on the trip if she and each friend
gets a snack pack with no leftovers? How many bananas and eggs will each person get?
5.
Suppose Mrs. Knouff also provides 18 bottles of water. Now each person will get the same number of bananas, eggs, and
water bottles. What is the largest number of snack packs she can make now? How many bananas, eggs, and water bottles
does each person get?
6.
The Hardin-Houston 6th grade is participating in Habitat for Humanity building houses for deserving families in Shelby
County. The 6th grade is helping install windows. The windows come in packs of 18 and window frames come in packs of
24. The 6th grade will need the same number of windows and window frames. How many windows and window frames will
they need? How many packs of windows and how many packs of window frames will this be? If they help build four
identical houses how many windows and frames are in each house?
7.
Due to all of the snow days, the Superintendent is asking all of the teachers to make Snow Day Learning Packets for the
students. The Superintendent gave Mrs. Knouff 56 Social Studies activities, 84 chapter books, and 140 math activities for
each of her classes. Mrs. Knouff will make identical packets with no leftovers for her classes. She will also makes the most
packets possible. How many packets will she be able to make for each of her classes? How many Social Studies activities,
chapter books, and math activities are in each packet?
8.
The I.B. Connect-n Computer Company recommends their customers to clean their temporary internet files every 45 days,
update their virus protection every 36 days, and run anti-virus programs every 27 days. How many days will pass until their
customers will need to do all three tasks at the same time?
9.
The cast of a play had a party. The drama teacher served 54 cookies and 36 cans of soda. Each cast member at the same
number of cookies and drank the same amount of soda. Nothing was left over. The drama teacher did not eat. What is the
greatest number of cast members that could have been at the party?
10. What is the mystery pair of numbers?
 Clue #1: The greatest common factor of the mystery pair is 7.
 Clue #2: The least common multiple of the mystery pair is 70.
 Clue #3: Each of the numbers in the mystery pair has two digits.
 Clue #4: One of the numbers in the mystery pair is odd. The other is even.