Finding the LCM (least common multiple)

and GCF (greatest common factor)

Prime factorize 24 and 16

24 16

2 x 12 4 x 4

4 x 3 2 x 2 2 x 2

2 x 2

Write the common factors where the Venn Diagram intersects.

24 = 2 x 2 x 2 x 3 16 = 2 x 2 x 2 x 2

Write the common factors where the Venn Diagram intersects.

24 = 2 x 2 x 2 x 3 16 = 2 x 2 x 2 x 2

2x2x2

Write the other factors of each number in the other side of the Venn

Diagram 24 = 2 x 2 x 2 x 3 16 = 2 x 2 x 2 x 2

2x2x23 2

The GCF is the product of the intersection2x2x2=8

24 = 2 x 2 x 2 x 3 16 = 2 x 2 x 2 x 2

2x2x23 2

The LCM is the product of all of the factors listed3x2x2x2x2=48

24 = 2 x 2 x 2 x 3 16 = 2 x 2 x 2 x 2

2x2x23 2

Prime factorize 45 and 36

45 36

5 x 9 6 x 6

3 x 3 3 x 2 3 x 2

Write the common factors where the Venn Diagram intersects.

45 = 3 x 3 x 5 36 = 2 x 2 x 3 x 3

Write the common factors where the Venn Diagram intersects.

45 = 3 x 3 x 5 36 = 2 x 2 x 3 x 3

3 x 3

Write the other factors of each number in the other side of the Venn

Diagram 45 = 3 x 3 x 5 36 = 2 x 2 x 3 x 3

3 x 35 2 x 2

The GCF is the product of the intersection3x3=9

45 = 3 x 3 x 5 36 = 2 x 2 x 3 x 3

3 x 35 2 x 2

The LCM is the product of all of the factors listed5x3x3x2x2=180

45 = 3 x 3 x 5 36 = 2 x 2 x 3 x 3

3 x 35 2 x 2

Now it’s your turn to try some more!!