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lcm of (a_1, a_2, ..., a_{18}) where sum a_1=665

Source: 2000 Moldova JBMO TST p2

February 20, 2021

number theoryleast common multipleSum

Problem Statement

The number

665

is represented as a sum of

18

natural numbers nenule

a_1, a_2, ..., a_{18}

. Determine the smallest possible value of the smallest common multiple of the numbers

a_1, a_2, ..., a_{18}