Find the smallest number that leaves a remainder of 5 when divided by 12, by 15 and by 20…

Step 1. Take away the remainder. The number minus $5$ is a common multiple of $12$, $15$ and $20$.

Step 2. LCM. $12 = 2^2 \times 3$, $15 = 3 \times 5$, $20 = 2^2 \times 5$, so LCM $= 2^2 \times 3 \times 5 = 60$.

Step 3. The smallest. $60 + 5 = 65$.

Step 4. The others. They are $60k + 5$: $65, 125, 185, 245, \ldots$ The first above $200$ is $245$.