let's say the numbers are "a" and "b".
we know that their GCF is 2, so 2 must be a factor of both, that leaves us with "2a" and "2b".
we know their LCM is 36, so we can divide 36 ÷ 2a = an integer, and we can also 36 ÷ 2b = an integer.
we know both "a" and "b" have a factor of 2, and the LCM is 36, so in the division, of 36 and either one, it can be simplified or reduced to just 18, namely 36 ÷ 2b, can be just 18 ÷ b, likewise 36 ÷ 2a can be written as just 18 ÷ a.
as a matter of an LCM, we could say that the product of "a" and "b" could give use that 18, so from the factors of 18, we can just pluck them out, let's do a quick prime factoring of 18.
18 = 2 * 3 * 3
so we can use a combination for two numbers from there of either 6 and 3, or 2 and 9.
so we can write those numbers as a = 2(6) = 12, b = 2(3) = 6.
or we can also write them as a = 2(2) = 4, b = 2(9) = 18.
either combination will work.
