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Home » \( A \approx 25 \times 3.14159 = 78.53975 \). - Treasure Valley Movers

\( A \approx 25 \times 3.14159 = 78.53975 \). - Treasure Valley Movers

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 The LCM is obtained by taking the highest powers of all primes that appear:

📌 Question: An electrical engineer is designing a smart grid system where power surges occur every $ n $ milliseconds, and $ n $ is the smallest positive integer that leaves a remainder of 3 when divided by 7 and a remainder of 4 when divided by 9. What is $ n $?

📌 Solution: We are given the system of congruences:

📌 We solve this using the method of successive substitutions or the Chinese Remainder Theorem. From the first congruence, write:

📌 We now find the modular inverse of 7 modulo 9. Testing small values:

📌 Substitute back into $ n = 7k + 3 $:

📌 n = 7(9m + 4) + 3 = 63m + 28 + 3 = 63m + 31

📌 The smallest positive $ n $ occurs when $ m = 0 $:

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