Number theory · Gcd and lcm · Euclidean algorithm · Divisibility rules · Modular arithmetic · Alternating digit sum
Let \(a = 123456789\) and \(b = 987654321\).
(1) Find \(\gcd(a, b)\).
(2) Find the remainder left by \(\operatorname{lcm}(a, b)\) on division by \(11\).
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Serbian Republic Competition (Republicko takmicenje) 1997, high school grade I, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source