Excerpted from bostonglobe.com:
When the Professor reminds a colleague “What happens to us as individuals is not of the least consequence,” we are jolted by the familiarity of the mind-set.
What does least consequence mean?
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As the comments says, it means "Is not important " or " won't influence anything".
We can think of it this way: something that happens to us as a result of something else is a consequence. The smallest possible consequence is the least consequence. And this? This is so unimportant it doesn't even have the smallest possible consequence.