Question

Does any pair of random numbers have a common multiple?

Answer 1

Yes any pair of random numbers will have a common multiple.
This can be shown by examples take any random number 2, 4. The common multiple will be 4, 8, 12....
If the numbers are prime then the common multiple will be their product.
For example 2, 3. The lowest common multiple is 6. So all random numbers will have a common multiple.