I am looking for real life applications of gcd. I have found one with tiles but there must be many more of these type.
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Suppose that you have two sets of people of cardinalities m,n and you want to divide them into teams of k people with every team being composed of people of only one of the original two sets. Then the maximum value of k where this is possible is $\gcd (m,n)$.
In fact if it is possible to do this with a specific k. Then $k |\gcd(m,n)$.