2-5-3-7 L Method for GCF and LCM

This is a new method in finding GCF and LCM.  You begin first by listing your two numbers side by side.  We chose 24 and 36.  Then, draw an upside down division house.

Start with 2.  If 2 is a factor of both, write it outside the house, then divide.  Put the quotient underneath your number.  For our example, 2 is a factor of both 24 and 36, so we put 12 and 18 under them, respectively.  Continue this process until you have only prime numbers OR 2-5-3-7 are no longer factors of what you have left.

The numbers on the left side represent the prime factor string GCF.  Multiply them together to find the GCF.

The "L" (left side and bottom) represent a factor string for LCM.  Multiply all of them together.

As you can see, 12 is the GCF for 24 and 36. 72 is the LCM for 24 and 36.

Here is another example with 30 and 50.  This time we have a 5.

This method can be done with 3 numbers as well.  Just place the 3rd number to the right.  However, you need to continue until at least two numbers are prime, even if you cannot decompose one of the 3 numbers left.  Just drop it down as is and continue.