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.

Question

Amity · Answer

108 and 72! I need points plz!

Maris · Answer

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 .

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