Thus, the maximum number of grants is $\boxed{15}$.

February 22, 2026

$Thus, the maximum number of grants is $\boxed{15}$.$

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$2025 = 3^4 \times 5^2$
$1515 = 3 \times 5 \times 101$
The $\gcd$ is the product of the smallest powers of common primes: $3^1 \times 5^1 = 15$.
Question: A spaceship’s navigation system uses a 13-bit code and a 17-bit engine control sequence. What is the smallest number of distinct sequences required to uniquely align both systems simultaneously?
Solution: The smallest number of distinct sequences is the least common multiple (LCM) of 13 and 17.
Since 13 and 17 are primes, $\text{LCM}(13, 17) = 13 \times 17 = 221$.

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