That's a fascinating story. Thank you for sharing.
As I went about my day, I couldn't get that story off my mind, and
I was astonished at the further implications, insinuations, inferences,
and ramifications that bubbled up from my challenged brain.
Although you have not asked for it, permit me to add one of my discoveries
to your succinct, innocent, and deceptively simple narrative:
==> The numbers are 37 and 38 !
12, 13 and 14
5, 6 and 7
8, 9, and 10
14, 15, 16
4,6,8
Find 3 consecutive numbers where the product of the smaller two numbers is 19 less than the square of the largest number.
The LCM of a set of numbers can never be smaller than the largest number in the set.
5,6,7
That is not possible
11,12,13
8,10,12
to find the range of numbers, you take the largest number and subtract the smaller number. 119-(-54)=119+54=173
1, 3, 5
16, 17 and 18
12, 13 and 14
8, 9, and 10
5, 6 and 7