FIND THE GCF (GREATES COMMON FACTOR) AND THE LCM (LEAST COMMON
MULTIPLE) OF 100, 150, 200

The least common multiple (other than 1) is easy, since each number is
divisible by two. 2 is the smallest multiple common to all 3 numbers.

One link I found shows the method to finding greatest common factors 

"Factoring - Greatest Common Factor (GCF) - First Glance" from
math.com
( http://www.math.com/school/subject1/lessons/S1U3L2GL.html )

It says to 

"1. List the prime factors of each number. 
 2. Multiply those factors both numbers have in common. 
    If there are no common prime factors, the GCF is 1."

So, for the problem given, the greatest common factor would be 50

100: 2*2*5*5
150: 2*3*5*5
200: 2*2*2*5*5

So, those multiples in common of each number would be: 2*5*5 or 50

I hope this fully answers your question. If anything is unclear,
please ask for a clarification and I will be glad to assist.

Search strategy:

://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&safe=off&q=greatest+common+factor

Hi skeeter1:

In a similar vein, the LCM (least common multiple) takes the values in
the prime factorizations and includes just enough factors such that
all the factors from each number can be found in the result. In other
words:

100: 2*2*5*5 
150: 2*3*5*5 
200: 2*2*2*5*5 

LCM(100,150,200) = 2*2*2*3*5*5 = 600

This is the smallest number that each of 100, 150, and 200 divide into
evenly.

websearcher-ga

Thanks websearcher for making up for my confusion. I must have been
thinking least common multiple was another name for least common
denominator. Again, thanks for helping in this matter.

No problem at all funkywizard. I just figured you missed that part of
the question. :-)

Anytime. 

websearcher-ga