4.4 Least Common Multiple
Vocabulary:
Multiple:
Common Multiple:
Least Common Multiple (LCM):
Least common denominator:
Example:
List 5 multiples of the following numbers.
a. 4
b. 6
Checkpoint: Finding Multiples
List 5 multiples of the following numbers.
1. 3
2. 7
3. 9
Explore on your own!
Choose two numbers less than 20
Write the first 10 multiples of each number
How many multiples are the same?
If more than one, which one is the smallest?
Finding The Least Common Multiple
LCM
Step1: List the multiples of each number
Step2: Find the smallest number they have in common
1) Find the LCM of 3 and 5
Step1:
Step2:
Example:
LCM of 12 and 20
Checkpoint:
1) Find the LCM of 4 and 6
2) Find the LCM of 12 and 16
How to find the least common multiple of monomials:
1. Factor each expression using exponents.
2. Find the product of the highest power of each factor
including the variable.
Things to remember:
If the variable is in either monomial it MUST be in the LCM
Example:
Find the LCM of 6xy and 16x2
Factor 6xy
Factor 16x2
Example:
Find the LCM of 6x2y and 9x4z
Factor 6x2y
Factor 9x4z
Checkpoint:
Find the LCM
1. 15x2, 27x
2. 6m2, 10m3
3. 14ab, 21bc
Finding the least common denominator (LCD):
1. Find the LCM of the denominators
2. That's it!
What do I do now.....
What did you have to multiply your denominator by to get the LCM?
You now must multiply the numerator by that same number!
Example:
How do we know if 1/6 or 7/15 is bigger?
1. They need to have the same denominator!
a. Find the LCD
Note: What you do the bottom of the fraction, you must also to the top!
When you multiply 6 x ___ = 30
When you multiply 15 x ___ = 30
Now we can compare! What is greater?
5/30 or 14/30
Hint: All you need to do is look at the numerator now since the
denominator is the same!!
Example:
Find the LCD of 1/4 and 2/7
Which fraction is larger?
1. Write the fractions and simplify
2. Find the LCD
3. Write equivalent fractions using LCD
4. Compare the numerators
Use the LCD to determine which fraction is greater.
a.
b.
c.
d.
Checkpoint!
Order the fractions from least to greatest
1. 2/3, 3/7, 5/2, 3 ½
2. 5/6, 4/3, 2/11, 4