I'm assuming, by the phrasing "array could be multiplied", that you must multiply all numbers in the array by the same factor in order to achieve integers everywhere.

Here's one algorithm:

Then is the number you're after.

Here's your three numbers as an example:

For , . Let Then (Check: an integer.)

For , . Let Then (Check: an integer.)

For , . Let Then (Check: an integer.)

Finally, let which certainly works for your situation. You could dream up an example where the final factor is less than that, but your numbers beyond the decimals would have to have more factors in common than your example.

Does this make sense?