At first glance, this seems like a "distance = rate x time" problem; however, it's actually a problem involving only the Least Common Multiple (LCM). We are not concerned with how far each travels; only with when their rates will allow their position to coincide again. To find the LCM of 14 and 12, we can complete a prime factorization of each.

Here, if we want to find the LCM of 14 and 12, we can produce a prime factorization of each number:

14: 2 x 7 (prime factorization)

12: 2 x 2 x 3 (prime factorization)

The product of the sets of primes with the highest exponent value of both of the two integers produces the following:

7 x 3 x 2^2 = 84, which is the LCM. We can interpret this to mean that it will take 84 minutes for them to reach the same spot.

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