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Home » Gardenias That Flash at You—Follow This Easy Care Rule for Stunning Blooms! - American Beagle Club

Gardenias That Flash at You—Follow This Easy Care Rule for Stunning Blooms! - American Beagle Club

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Therefore, the product \( n(n+1)(n+2) \) is divisible by the least common multiple of 4 and 3, which is:

📌 \text{lcm}(4, 3) = 12

📌 We can confirm this by testing specific cases (like 1, 2, 3 or 2, 3, 4) where the product is divisible by 6 but also by 12 in certain configurations (like 3, 4, 5).

📌 Thus, the largest integer that must divide the product of any three consecutive integers is:

📌 How many lattice points lie on the line segment joining (1, 2) and (7, 8)?

📌 Lattice points on a line segment between two points \((x_1, y_1)\) and \((x_2, y_2)\) are integer-coordinate points on the segment. The number of such points (including endpoints) is given by:

📌 \gcd(x_2 - x_1, y_2 - y_1) + 1

📌 where \(\gcd\) denotes the greatest common divisor.

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