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OpenStudy (anonymous):
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?
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OpenStudy (academicgurusinc):
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 If you found this helpful, I encourage to subscribe to our youtube channel https://www.youtube.com/channel/UCYiI7SmkU4_vhdSzKBWsifg to stay current with all of our new videos. Regards, Academic Gurus Inc. Twitter (@Academic_Gurus) Facebook (AcademicGurusInc) Youtube (Academic Gurus Inc)
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