Using a Venn Diagram to find the Greatest Common Factor and the Least Common Multiple
24                                       40


                        2

                        2

                          2
                      

  3                                               5                            
The above Venn was created by factoring the number 24 by using the rules of divisibility to find:

2l  24
  2l12
    2l6
       3l 3
           1

The same process was used for 40 to see

2l 40
  2l 20
   2l 10
     5l 5
          1

Now put all the common factors in the center of the Venn 2 x 2 x 2 =8
So 8 is the GCF

Multiply all the factors in the complete diagram to get 40 x 3= 120
for the Least Common multiple

DO YOU SEE THAT 3/5 is looking right at you for the simplified version of  24/40.  WHY?

Is it because when you divide out the GCF of 8 into the 24 you get 3 and 8 into 40 is 5?