Problem
NT-B1-M08-P008 Compatible System
#8
★★☆☆☆ Level 2 of 5
Solve \(x\equiv5\pmod8\), \(x\equiv9\pmod{12}\).
Check residues modulo \(\gcd(8,12)=4\).
The residues \(5\) and \(9\) are both \(1\) modulo \(4\), so the system is compatible. Check \(5,13,21,\ldots\) modulo \(8\); \(21\equiv9\pmod{12}\). The answer is \(x\equiv21\pmod{24}\).
The answer is modulo the LCM, not the product.