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LCM identity with combinations

Source: Indian Postal Coaching 2008 set 3 p1

May 25, 2020
number theoryleast common multipleLCMCombinations

Problem Statement

Prove that for any n≥1n \ge 1,
LCM0≤k≤n{LCM _{0\le k\le n} \big \{ (nk)n \choose k }=1n+1LCM{1,2,3,...,n+1}\big\} = \frac{1}{n + 1} LCM \{1, 2,3,...,n + 1\}
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