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Home » How Black Flip Flops Are Becoming the Ultimate Summer Fashion Must-Have! - Databee Business Systems

How Black Flip Flops Are Becoming the Ultimate Summer Fashion Must-Have! - Databee Business Systems

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question: What is the remainder when the sum $1^3 + 2^3 + \dots + 12^3$ is divided by 13, analogous to calculating the total drug dosage cycles over 12 phases?

📌 Solution: The sum of cubes formula is $\left(\frac{n(n+1)}{2}\right)^2$. For $n = 12$, the sum is $\left(\frac{12 \cdot 13}{2}\right)^2 = (78)^2 = 6084$. Dividing by 13: $6084 \div 13 = 468$ with remainder 0, since $13 \cdot 468 = 6084$.

📌 Question: What is the smallest three-digit number divisible by 14 and 21, representing the minimal batch size for synchronized seismic sensor calibration?

📌 Solution: The least common multiple (LCM) of 14 and 21 is $42$. The smallest three-digit multiple of 42 is $42 \times 3 = 126$.

📌 \boxed{126}

📌 Question: What is the least common multiple of 16 and 24, analogous to synchronizing two drug delivery cycles with half-lives?

📌 Solution: Prime factorization: $16 = 2^4$, $24 = 2^3 \cdot 3$. LCM takes the highest powers: $2^4 \cdot 3 = 16 \cdot 3 = 48$.

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