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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:

 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:

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