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LCM: (Least Common Multiple)

 

The two most common methods of finding the LCM of two numbers are the Listing method and the Prime Factorization method.

 

The Listing Method:  List the multiples of the larger number until you find a common product that is divisible by the smaller number. 

Example:  To find the least common multiple of 6 and 8:

Text Box: Once you have listed the first three values, you should notice that 6 goes into 24, so 24 is the LCM of 6 and 8

 8

6

16

12

24

18

 

24

  

The Prime Factorization Method:  This method is most useful if the numbers that you are trying to determine their LCM is very large.

 

Example: Find the LCM of 36 and 90:

 Step 1: Find the prime factorization of both numbers:

 Text Box: 36 
6                  6
     2          3       2        3 
                22  32
Text Box: 90 
9                  10
     3          3       2         5 
                2  32  5

 

 

  

 

 Step 2:  List all the base numbers of the factors.  As you see from above, you have a 2, 3, and a 5.  Take the largest exponential value of all these numbers and multiply them. 

            Look you have 22 and 2 take the 22. (only once)

            Next you have 32 take the 32   (only once)

            Next you have a 5 take the 5

Multiply all the values that you have taken:

    2 2 32 5 =

                          4 9 5 =

                                  45 5 = 180  so the LCM is 180