Final answer:
The three-digit number you are looking for is 210 because it is a multiple of 2, 5, and 7, has a sum of digits equal to 10, and is not 280.
Step-by-step explanation:
You are trying to identify a three-digit number that is a multiple of 2, 5, and 7, has a sum of digits equal to 10, and is not 280. The fact that it is a multiple of 2 and 5 means it must end in 0. Because it is also a multiple of 7, we need to find a multiple of 70 that has a three-digit number and a digit sum of 10. Starting from 70 and adding 70 each time, we look for a number that meets our conditions. The first few multiples of 70 are 140, 210, 280, 350, 420, and so on. Of these, only 210 and 280 have digit sums that add up to 10. Since 280 is excluded, the number can only be 210.