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Home » The LCM is found by taking the highest powers of all primes: - American Beagle Club

The LCM is found by taking the highest powers of all primes: - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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Unless the "largest" is not 729, but the sequence starts with capacity...
Alternative: The first bottle used has capacity 729, but we only fill...
Given ambiguity, assume standard geometric series: total volume to be...
But total is \(S = a / (1 - r) = a / (1 - 1/2) = 2a\)
Set \(2a = 729\) → \(a = 364.5\)
Then bottles: 364.5, 182.25, 91.125, 45.5625, 22.78125, 11.390625, 5.6...
Sum after n terms: \(S_n = a(1 - (1/2)^n)/(1 - 1/2) = 2a(1 - 2^{-n})\)
Set \(2a = 729\), so \(S_n = 729(1 - 2^{-n})\)
We want to fill 729 ml, so \(729(1 - 2^{-n}) \geq 729\) → only when n→...
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