7th Grade Chapter 4.9 Least Common Multiple
Suppose a traffic light on one street turns red every 40 seconds and second light turns red ever 60
seconds. If both lights just turned red, in how many seconds will both lights turn red at the same time
again?
Light A: 40. 80. 120. 160
Light B: 60, 120, 180, 240
Both lights will turn red again in 120 seconds.
We just made 2 lists of multiples. For Light A we listed multiples of 40 and for Light B we listed
multiples of 60.
A multiple is the product of the number and any whole number.
EX. List the multiples of 6: 6, 12, 18, 24, 30 …
You Try: List the multiples of 9: 9, 18, 27, 36, 45…
How many multiples could we make for each number? Infinite, since you can keep multiplying
numbers.
Our goal today is to find the least common multiple of 2 or more numbers.
The least common multiple (LCM) of two or more numbers is the least of their common multiples.
We can find the LCM in two ways:
Method 1: Make a list
Multiples of 6: 6, 12, 18, 24, 36 …
Multiples of 9: 9, 18, 27, 36 ….
The common multiples (multiples shared by each number) are 18 and 36.
Since 18 < 36, the LCM = 18
You Try: Find the LCM of 12, 16 LCM = 48
Method 2: Use Prime Factorization
1) Take the prime factorization of each number
2) Count the maximum number of times each factor appears in either number
3) Multiply all of those factors to find the LCM
EX Find the LCM of 9, 12, and 15 LCM = 180
EX 2 Find the LCM of 6, 10, and 15 LCM = 30
Worksheets
Brandon, Kani, and Wilfredo are handing out flyers for the local Clown College by going door to door.
They are all starting at the beginning of a block. Brandon drops off a flyer to every second house, Kani
drops one off at every third house, and Wilfredo gives one to every fourth house. Which house will
get all three flyers?
Final Question: Find the LCM of 8, 10, and 12 by using prime factorization
HW – Chapter 4.9 Pg. 171 # 11 – 33 all