Answer:
108 and 72
Step-by-step explanation:
You are given ...
GCF +LCM = 252
GCF -LCM = 180
2×GCF = 432 . . . . . add the two equations
GCF = 216
Then the LCM is 216 -180 = 36
This is what your problem statement says. Usually, we expect the least multiple to be somewhat larger than the greatest factor.
_____
If we assume the problem statement intends that the sum and difference between the LCM and the GCF are 252 and 180, respectively, then ...
GCF = 36
LCM = 216
The product of the unique factors is 216/36 = 6. The ratio of the unique factors is 1.5 : 1 = 3 : 2. That is, the unique factors are 3 and 2, and the numbers are ...
3(36) = 108 and 2(36) = 72
The two numbers are 108 and 72.
