The LCM Of Two Numbers Is 72. The GCF Is 12. They Differ By 12?

LCM X GCF = the product of the two numbers  ----> this is a rule if you want later we may prove it.

Using the given information we can have two equations:

Let n be the first number
let m be the second number

equation (1) mxn = 72x12  ------> mxn = 864
equation (2) m-n = 12  ------> m = 12 + n

replace equation (2) in (1) and you'll have (12 + n)(n) = 864

distribute on the left side to get : 12n + n^2 = 864

make them one equation: N^2 + 12n  - 864 = 0

Factor the left side to get (n + 36)(n - 24)=0

so n = -36 or n = 24

then you replace in equation (2) to get the value of m = -24 or m = 36

so we have two possible answers (-36, -24) or (36, 24)