Students typically start learning about GCF and LCM in sixth grade. They learn that GCF is the biggest factor that can go evenly -- without a remainder -- into each of the numbers in their set. They also learn that LCM is the smallest number that each of their numbers in their set can go into evenly. For example, for the numbers 16 and 24, the GCF is 8 and the LCM is 48.
Draw a ladder that is lying vertically. Place the two numbers in your set in the space between the top two rungs of your ladder. Find a number that goes into each of the numbers in your set without a remainder, and write it on the left side of your ladder. Divide each of your starting numbers by the number on the left and place the resulting numbers in the space between the second and third rungs. Repeat this process by placing your common factor on the left of the numbers being divided and the results in the next row down. When the only number your results have in common is 1, you are ready to calculate the GCF and LCM.
To find the GCF of the numbers in your set, multiply the numbers to the left of your ladder. So, for 16 and 24, your ladder may look like this:
2 |16 and 24
4 |8 and 12
1 |2 and 3
To find the GCF of 16 and 24, which is 8, multiply 2 x 4 x 1. Alternatively, start the ladder method by dividing 16 and 24 by 8 or 4.
To find the LCM, multiply the numbers on the left of your ladder, as you did to find the GCF, and by each of the numbers in the last row of your ladder. For example:
2 |16 and 24
4 |8 and 12
1 |2 and 3
So, the LCM for 16 and 24 is (2 x 4 x 1) x (2 x 3) or 48.
When you teach GCF and LCM to kids by presenting them with simple definitions and the ladder method, you take away some of the intimidation they might first feel upon hearing the names of these concepts. You also prepare them for using GCF and LCM for math they will learn later such as using the GCF to reduce a fraction.