Let me know if this is correct :

(1)Finding the lcm using which ever method for:5,15 , and 20

8:2x2x2x3x5x5
15:2x2x2x3x5x5
20:2x2x2x3x5x5
---------------
LCM:2x2x2x3x5x5
After simplification LCM:120

(2)Find the GCF for each of the following numbers: 36, 64, 180

Prime Factors
36=2x2x3x3x1
64=2x2x2x2x2x2x1
180=2x2x3x3x5x1
Common Prime Factors
36= 2x2x2
64=2x2x2
180=2x2x2

GCF=4

I am not certain what your logic is, but the answers are correct.

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