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Home » The product of the smallest and largest is 26 × 30 = 780. - Abu Waleed Tea

The product of the smallest and largest is 26 × 30 = 780. - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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\gcd(5^m - 1, 5^n - 1) = 5^{\gcd(m,n)} - 1.
We compute $ \gcd(24, 36) $. Using the Euclidean algorithm:
\gcd(36, 24) = \gcd(24, 12) = \gcd(12, 0) = 12.
\gcd(5^{24} - 1, 5^{36} - 1) = 5^{12} - 1.
We now compute $ 5^{12} - 1 $:
5^2 = 25, \quad 5^4 = (25)^2 = 625, \quad 5^8 = 625^2 = 390625,
5^{12} = 5^8 \cdot 5^4 = 390625 \cdot 625.
We compute $ 390625 \cdot 625 $:
Break $ 625 = 600 + 25 $, so
\cdot 600 = 390625 \cdot 6 \cdot 100 = (2,343,750) \cdot 100 = 234,375...

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