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min LCM of distinct a, b, c, d if a + b + c + d = 1000

Source: 2019 Dürer Math Competition Finals Day2 E11 E+10 https://artofproblemsolving.com/community/c1621835_2019_

January 5, 2022
least common multipleLCMnumber theory

Problem Statement

What is the smallest possible value of the least common multiple of a,b,c,da, b, c, d if we know that these four numbers are distinct and a+b+c+d=1000a + b + c + d = 1000?
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