They could be: 17 and 149
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10 and 35
6 and 126 and 1812 and 18
As written, no numbers satisfy those conditions. 6 and 36 have a GCF of 6 and an LCM of 36.
The LCM of two numbers is one of the numbers when one of the numbers is a multiple of the other. The LCM of two numbers is the product of the numbers when they are relatively prime. In all other cases (like consecutive even numbers that aren't 2 and 4) the LCM is as you describe.
Two or more numbers are needed to find their LCM