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When finding multiples, you can list all of the products after multiplying it by 1, 2, 3, 4…
Finding the Least Common Multiple
For example,Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, …
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, …
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, …
DISCUSS: For the multiples of 4, 6, and 8, which multiples are common with all three?
Finding the Least Common MultipleMultiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, …
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, …
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, …
So, we see a common multiple of 24, but there are more common multiples.
Since 24 is the smallest value of all of the common multiples, it is considered the Least
Common Multiple for 4, 6, and 8.
Using the Cake Method to find LCMFind the LCM for 4 and 6
4 6
The LCM is 12.
2
2 3
2 • 2 • 3
Multiply all of the side numbers AND the last row to find the LCM
Using the Cake Method to find LCMFind the LCM for 4a3b and 6a2c
4a3b 6a2c
The LCM is 12a3bc.
2
2a3b 3a2c
2 • a • a • 2ab • 3c
a
2a2b 3aca
2ab 3c
Finding the LCM of three or more numbersFind the LCM for 4, 6, and 8
4 6
The LCM is 24.
2
2 3
2 • 2 • 3
First find the LCM of two of the numbers
12 84
3 2
Then use the first LCM and the third number
LCM is 12
4 • 3 • 2
You try: Find the LCM of 125, 500
500
You try: Find the LCM of
4 4 6 23 ,7m n m n
6 421m n
Homework
• Page 231 (20-42) even(ignore the directions in the book and just use
the cake method to find the LCM)