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GCD & LCMhard
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Solve the system of congruences using the Chinese Remainder Theorem: \begin{align} x &\equiv 1 \pmod{4}\ x &\equiv 2 \pmod{3}\ x &\equiv 3 \pmod{5} \end{align} What is x mod 60x \bmod{60}xmod60 (where 60=lcm(4,3,5)60 = \text{lcm}(4, 3, 5)60=lcm(4,3,5))?