find the two digit numbers which have GCD=6 and LCM=432.
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432/6 = 72, which can be factored as
.. 72 = 1*72 = 2*36 = 3*24 = 4*18 = 6*12 = 8*9
We need to choose factor pairs that have no common factors. These are (1,72) and (8,9). Then possibilities for your numbers are
.. 1*6 = 6 and 6*72 = 432
or
.. 8*6 = 48 and 6*9 = 54
.. 72 = 1*72 = 2*36 = 3*24 = 4*18 = 6*12 = 8*9
We need to choose factor pairs that have no common factors. These are (1,72) and (8,9). Then possibilities for your numbers are
.. 1*6 = 6 and 6*72 = 432
or
.. 8*6 = 48 and 6*9 = 54
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