Transcript Common Multiples

REVIEW – Greatest Common Factor
The Greatest Common Factor is the biggest number
that can be divided into two ore more numbers.
It is also called the greatest common divisor.
It is called greatest common factor because factor
of a number is a factor is a number that another number is divisible
by. Even though is called the “Greatest”, it cannot be bigger than
the smaller of the two numbers, since larger numbers could not be
divided into it.
4 is the Greatest Common Factor of 12 and 16 because it is the
biggest number that 12 is divisibly by and 16 is divisible by.
12 is the Greatest Common Factor of 12 and 48 because 12 is the
biggest number that 12 is divisible by and that 48 is divisible by.
Another way to do this is the Birthday Cake Method.
Multiply the numbers on the left side of the birthday cake.
In the example, multiply 2 x 2 x 3. This will give you a GCF of 12.
LEAST COMMMON MULTIPLE
Here’s a funny video clip:
http://mathdogmedia.blogspot.com/2013/01/lcm-father-of-bride.html
The least common multiple is the smallest multiple that is in common
between 2 or more numbers.
What are Multiples?
Multiples are products of a number and another number.
The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, ….
it goes on forever!
The multiples of 3 are : 3, 6, 9, 12, 15, 18, 21, 24, ….
The multiples of 4 are: 4, 8, 12, 16 20, 24, 28, …..
And so on…
What is the LEAST COMMON MULTIPLE of 12 and 48?
Multiples of 12: 12, 24, 36, 48, …
Multiples of 48: 48, 96,…
The first multiple in common is 48, so the LCM is 48.
Birthday Cake Method:
Multiply all of the numbers on the outside of the birthday cake, going
down the left side and across the bottom. Follow the “L” for LCM.
In the example, multiply 2 x 2 x 3 x 1 x 4. So, the LCM is 48.
What is the LEAST COMMON MULTIPLE of 9 and 12?
Find the LCM of 6 and 7
The LCM of 3 or more numbers can also be found. You can keep
building your cake as long as 2 of the numbers have a common factor.
Just bring the other number down to the next layer.
Find the LCM of 4, 6, and 16
2 4 6 16
2 2 3 8
1
3
4
In the second layer of the cake,
2 and 8 have a common factor, but 3 does
not have a factor in common with either one.
Just drop the 3 down to the next level.
Now none of them have a common factor, so
You are done. Make a big L and the product
of all those factors is the LCM!
LCM = 2 x 2 x 1 x 3 x 4 = 48
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48…
Multiples of 6: 6, 12, 18, 24 30, 36, 42, 48,…
Multiples of 16: 16, 32, 48, …
The smallest common multiple of all three numbers is 48.
Find the LCM of 12, 18, and 24
2 12
3 6
2
2
1
18 24
9
12
3 4
3
2
In the third layer of the cake,
2 and 4 have a common factor, but 3 does
not have a factor in common with either one.
Just drop the 3 down to the next level.
Now none of them have a common factor, so
You are done. Make a big L and the product
of all those factors is the LCM!
LCM = 2 x 3 x 2 x 1 x 3 x 2 = 144
Greatest Common Factor and Least Common Multiple Word Problems
1. A math teacher and a science teacher combine their first period classes for a
group activity. The math class has 24 students and the science class has 16
students. The students need to divide themselves into groups of the same size.
Each group must have the same number of math students. Find the greatest
number of groups possible.
2. A photography club is practicing developing techniques. One set of negatives
contains 32 negatives and another contains 28 negatives. Each set can be
divided
equally among the members present. List all the possible numbers of members
present. What is the greatest possible number?
3. Organizers for a middle school culmination have set up chairs in two sections.
They put 126 chairs for graduates in the front section and 588 chairs for
guests in the back section.
If all rows have the same number of chairs, what is the greatest number of
chairs
possible?
4. A quality control inspector in an egg factory checks every 36th egg for cracks
and every 42nd egg for weight.
What is the number of the first egg each day that the inspector checks for
both
qualities? (Hint: think this will be the least number....)
5. The manager at Frank's Snack Shack buys hot dogs in packages of 30. He
buys hot dog buns in packages of 24. Unfortunately, he cannot buy part of a
package.
What is the least number of packages of each product he can buy to have an
equal number of hot dogs and hot dog buns? (Careful: What is the question
asking for??)
6.Pepe enjoys bird-watching and observed two types of birds traveling this
season: ducks and seagulls. While the ducks traveled in flocks of 15, the seagulls
traveled in flocks of 12. If Pepe observed the same total number of ducks and
seagulls, what is the smallest number of ducks that he could have observed?