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3

Part of 2023 South Africa National Olympiad

Problems(1)

GCD and LCM

Source: The South African Mathematical Olympiad Third Round 2023 P3

7/30/2023
Consider 22 positive integers a,ba,b such that a+2b=2020a+2b=2020. (a) Determine the largest possible value of the greatest common divisor of aa and bb. (b) Determine the smallest possible value of the least common multiple of aa and bb.
number theorygreatest common divisorleast common multiple