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Home » For \(2\), the highest power is \(2^2\) - Red Crowns

For \(2\), the highest power is \(2^2\) - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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Consider three consecutive integers denoted as \( n, n+1, n+2 \).
Among any three consecutive integers, one must be divisible by 2 (sinc...
Among any three consecutive integers, one must be divisible by 3 (sinc...
Thus, the product \( n(n+1)(n+2) \) is divisible by both 2 and 3. Ther...
Additionally, consider the divisibility by 4. Among any three consecut...
Therefore, the product \( n(n+1)(n+2) \) is divisible by the least com...
\text{lcm}(4, 3) = 12
We can confirm this by testing specific cases (like 1, 2, 3 or 2, 3, 4...
Thus, the largest integer that must divide the product of any three co...
How many lattice points lie on the line segment joining (1, 2) and (7,...

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