To answer this question, you must take a look at your company and your stakeholders:
- Can the company afford to fund a project that is late just so that it is finished faster and to scope? If yes, then, in this case, the budget is the least important constraint.
- Can your stakeholders easily accept reduction of the scope just so that the project gets done on time and budget? If yes, then quality is the least important constraint.
- Can your client/project sponsor/stakeholders afford to have delays on the project and prefer to have delays rather than paying more or reducing the quality? If yes, then the schedule is the least important.
As you can see from the above, the least important constraint varies from one project to the other.