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Home » $8 = 2^3$, - iBuildNew

$8 = 2^3$, - iBuildNew

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 A programmer is developing an AI application that requires processing data packets. If the application handles packets every 18 seconds and another system processes every 24 seconds, what is the least common multiple of these two processing times?

📌 To find the least common multiple (LCM) of 18 and 24, we first determine their prime factorizations:

📌 \[ 18 = 2 \times 3^2 \]

📌 \[ 24 = 2^3 \times 3 \]

📌 The LCM is found by taking the highest power of all prime factors:

📌 Highest powers: \(2^3\), \(3^2\)

📌 \[ 2^3 \times 3^2 = 8 \times 9 = 72 \]

📌 The least common multiple of the processing times is \(\boxed{72}\).

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