Exactly, in your case it'd be 71.
And I'm not sure how to explain the reason why you use LCM instead of GCD
In this case it also has a bit of common sense, because if you had used GCD in the original problem, his age would be 2 because the GCD of those numbers is 1, and it already says that his age can be divided by 2, 3, 4, 5 and 6, and have a reminder of 1, so it wouldn't make sense