Question

Let m and n be positive integers such that m = 24n + 51. What is the largest possible value of the greatest common divisor of 2m and 3n?

Answer 1

Notice that we can write 2m as 48n+102. Notice that using the Euclidean Algorithm, we can reduce this to the greatest common divisor of 102 and 3n. Obviously, the greatest possible value of the greatest common divisor of $102$ and anything is 102

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