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GCD and LCM

Source: The South African Mathematical Olympiad Third Round 2023 P3

July 30, 2023
number theorygreatest common divisorleast common multiple

Problem Statement

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.
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