A - GCF
What is the GCF (2,6)
2
LCM (4,5)
20
There are 65 representatives and 100 senators serving in the United States Congress. How many identical groups with the same numbers of representatives and senators could be formed from all of Congress if we want the largest groups possible?
5 IDENTICAL groups (GCF)
Hot dogs come packed 10 in a package. Hot dog buns come packed 8 in a package. If we want one hot dog for each bun for a picnic with none left over, what is the least amount of each item of food we need to buy?
we need to buy 40 hot dog buns and 40 hot dogs
The PTA placed a trail marker in the ground every four hundred yards. Every nine hundred yards, the PTA set up a water station. What is the shortest distance a runner will have to run to see both a water station and trail marker at the same location?
36 hundred yards then a runner will see a water station and trail marker at the same place (LCM)
GCF (8,100)
4
LCM(6,36)
36
Is the GCF of a pair of numbers ever equal to one of the numbers? Explain with an example.
THERE ARE LOTS OF CORRECT EXAMPLES!!!! Yes the GCF (4,16) is 4 because 4 is the biggest number that goes into 4 and 16
STOP!! YOU MUST DO 100 FIRST!!!
How many packages of each item would we have to buy?
4 Packs of hot dogs
5 packs of buns
Timmy is shopping for a dance party. His donation to the party is fruit snacks and sodas. Fruit Snacks come in packages of 12, and sodas come in a package of 10. What is the fewest number of packages of each product Timmy must purchase so that he has the same number of fruit snacks and sodas?
Jimmy needs 5 packs of fruit snacks and 6 packs of soda (find LCM then divide)
GCF(5,19)
1
LCM(11,7)
77
There are 18 girls and 24 boys who want to participate in a Trivia Challenge. If each team must have the same ratio of girls and boys, what is the greatest number of teams that can enter?
6 teams (GCF)
Starting at 6:00 a.m., a bus stops at my street corner every 15 minutes. Also starting at 6:00 a.m., a taxi cab comes by every 12 minutes. What is the next time both a bus and a taxi are at the corner at the same time?
7:00 am
(lcm is 60) so in 60 minutes the bus will be at the street corner again
Gary found 72 shells and 40 coins at the beach. He wants to give them to some of his friends. Each friend will receive the same number of shells and the same number of coins. What is the greatest number of friends Gary can give shells and coins to?
He can give coins to 8 friends
GCF(96,88)
8
LCM(5,7)
35
You must do the 300 one first after you've done it
Find how many boys and girls each team would have.
3 Girls per team
4 boys per team
Two gears in a machine are aligned by a mark drawn from the center of one gear to the center of the other. If the first gear has 15 teeth, and the second gear has 9 teeth, how many revolutions of the first gear are needed until the marks line up again?
45 revolutions
STOP you need to do 300 first
How many shells will each friend receive? How many coins?
Each friend will receive 9 shells
each friend will receive 5 coins
GCF(36,48)
12
LCM(12,8)
24
Ski Club members are preparing identical welcome kits for new skiers. The Ski Club has 60 hand-warmer packets and 48 foot-warmer packets. Find the greatest number of identical kits they can prepare using all of the hand-warmer and foot-warmer packets. How many hand-warmer packets and foot-warmer packets would each welcome kit have?
GCF-12 identical kits
5 hand warmers
4 footwarmer packs per welcome kit
Is the LCM of a pair of numbers ever less than both numbers? Explain with an example.
No because a multiple is never smaller than the number for examples the multiples of 4 are 4,8,12,16,20,....... there is no multiple less than 4
One container of gelato holds 9 scoops of gelato. One package of gelato bowls has 12 bowls. We want to make the fewest number of gelato bowls, with one scoop of gelato in each bowl and no gelato or bowls left over.
How many containers of gelato and packages of bowls should be purchased?
Fewest number of scoops with no gelato left over is 36 (this is the lcm)
we need 4 containers of gelato and 3 packs of gelato bowls