Find the greatest number that divides 301, 492 and 783, leaving remainders 5, 11 and 6 respectively.

Subtract the remainders: 296, 481 and 777 must be exact multiples. $296=8\times 37,481=13\times 37$ and $777=21\times 37$, and 8, 13, 21 have no common factor, so the answer is 37 (larger than every remainder, as needed).