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Using the example “Find the GCF of 24 and 36.”
Write the numbers inside an upside down division box as shown below:
Ask the students to identify a number that is a factor of both. For example, let’s say a student identifies
the factor of 4 that divides into both evenly. Record the 4 on the outside of the box, and record the
quotients below as shown:
Ask the students to identify a factor of both 6 & 9. A student might say that 3 is a factor of both 6 & 9.
Record the 3 and the quotients as shown.
Ask the students if there is a common factor for both 2 & 3. Once the class agrees that there is not one
(other than 1), inform the class that we have reached the endpoint. The GCF can be found by
multiplying the numbers on the left hand side, as shown below:
By multiplying 4 x 3, we find that the GCF of 24 & 36 is 12. This method works regardless of the
numbers chosen by the students. For example, you could have started with a 2 as a common factor
rather than 4, and the result would have been the same.
Using the same example finding the LCM of 24 & 36 is more visual
The process is the same
You multiply the left and bottom numbers, notice it looks like an “L” for LCM
By multiplying 3 x 4 x 2 x 3 we find the LCM is 72