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Question

The sum and the difference between the GCF and the LCM of two numbers is 252 and 180 respectivley. Find the 2 numbers if one is 1.5 greater than the other.

Answer

The two numbers are 108 and 72, respectively. Step-by-step explanation: Given the equations GCF + LCM = 252 and GCF - LCM = 180, we can solve for GCF by adding these two equations, which gives us 2×GCF = 432. Therefore, GCF = 216. The problem statement says that the LCM minus the GCF is 180, so the LCM would be 216 - 180 = 36, according to the statement. However, it is usually expected that the LCM is larger than the GCF, so if we assume that the sum and difference between the LCM and the GCF are 252 and 180, respectively, then we get GCF = 36 and LCM = 216. The product of the unique factors is 216/36 = 6, and the ratio of the unique factors is 3 : 2. Therefore, the unique factors are 3 and 2, which gives us 3(36) = 108 and 2(36) = 72. Hence, the two numbers are 108 and 72.