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)