10. Find the greatest and the least three-digit numbers, each of which is divisible by 6 and has the digit 7 in its representation.
10. Each of the sought numbers must end in an even digit (since it is divisible by 6), so the digit 7 cannot be at the far right. To make the number the largest (smallest), the hundreds digit should be the largest (smallest) of the possible ones. Taking into account the condition of divisibility by 3, we get the sought numbers 978 and 174.