Final answer:
To find a three-digit number divisible by 6 using the digits 1, 2, 5, and 7, we determine the number 726 satisfies the conditions, since it is even and the sum of its digits is divisible by 3.
Step-by-step explanation:
The question involves finding a three-digit number that is divisible by 6 and is composed of the digits 1, 2, 5, and 7. To satisfy this condition, a number must be divisible by both 2 and 3. Being divisible by 2 means the number must end in an even digit, so our options are 2 or 6 (since we cannot form a three-digit number with 1, 5, or 7 at the end). To check divisibility by 3, we look at the sum of the digits of the number, which must be a multiple of 3. After testing various combinations of the digits 1, 2, 5, and 7, we find that the number 726 satisfies both conditions. It is an even number (ending in 6), and the sum of its digits (7 + 2 + 6 = 15) is divisible by 3.