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Home » 2! Rare Images Reveal Implantation Blood: What Every Expecting Mother Should See! - DNSFLEX

2! Rare Images Reveal Implantation Blood: What Every Expecting Mother Should See! - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 #### 9.7Question: What is the largest possible value of $\gcd(a,b)$ if the sum of two positive integers $a$ and $b$ is 2025, representing the total number of seismic tremors recorded over two consecutive years?

📌 Solution: Let $a + b = 2025$. The greatest common divisor $\gcd(a, b)$ must divide $a + b = 2025$. The maximum possible value of $\gcd(a, b)$ occurs when $a$ and $b$ are both multiples of the largest divisor of 2025. Since $2025 = 45^2 = 3^4 \cdot 5^2$, its largest proper divisor is $2025 / 3 = 675$. Thus, $\gcd(a, b) = 675$ when $a = 675$ and $b = 1350$.

📌 \boxed{675}

📌 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}

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