LCM _FInd_LCM 102015woAB.docx
How to find the LCM of 2 numbers1
LCM = Least Common Multiple. The smallest multiple of some numbers.
Example:
FIND THE LCM of 10 and 25.
Step 1. Find the prime factorizations of each: (Use the trees for bigger numbers.)
10 = 2 x 5
25 = 5 x 5
Step 2. Start with one of the number’s factors for the LCM product. I start with 10’s factors
LCM = 2 x 5
Step 3. Complete the LCM product by answering this question:
What is a minimal way to tack onto this product some (or all or none) of the other number’s
factors such that all of the factors of both numbers are in the product? (in bold below):
LCM = 2 x 5 x 5
So I tacked on one more 5 to get LCM = 2 x 5 x 5 and see that now 25’s factors are in it.
LCM = 2 x 5 x 5 = 50 (answer)
In summary:
Notice: 10’s factors are in it because that is what I started with:
LCM = 2 X 5 X 5
And 25’s factors are also in it because I tacked on one more 5:
LCM = 2 X 5 X 5
So both numbers’ factors are n it and the LCM was found in a minimal way.
(Note: It is INCORRECT to say LCM = 2 x 5 x 5 x 5 = 250. Although both numbers’ factors are in
it, it is the most minimal way.)
1
The procedure is extended in similar fashion for more than 2 numbers