A number leaves remainder 7 when divided by 12, and also leaves remainder 7 when divided by 18. What is the smallest such number greater than 100?

Taking the common remainder away makes the number exactly divisible by both 12 and 18, so the number is 7 more than a multiple of LCM(12, 18) = 36. The candidates run 7, 43, 79, 115, 151, … and the first one past 100 is 115. Check: $115=12\times 9+7=18\times 6+7$. The trap is 151 — it satisfies both conditions perfectly well, but it is the next candidate up, not the smallest. Meanwhile 103 leaves remainder 7 on division by 12 but 13 on division by 18, and 108 is a multiple of both.