Final answer:
To find the least number that satisfies the given conditions, we can use the concept of the least common multiple (LCM) and continue adding multiples of the LCM until we find a number that satisfies all the conditions. The correct answer is 235.
Step-by-step explanation:
To find the least number that satisfies the given conditions, we need to find the smallest number that leaves a remainder of 7 when divided by 12, a remainder of 10 when divided by 15, and a remainder of 11 when divided by 16.
We can solve this problem using the concept of the least common multiple (LCM). The LCM of 12, 15, and 16 is 240. Therefore, any number that leaves the desired remainders when divided by 12, 15, and 16 must be a multiple of 240.
The smallest multiple of 240 that satisfies the conditions is 240 + 7 = 247. However, this number does not leave a remainder of 10 when divided by 15. So, we continue adding multiples of 240 until we find a number that satisfies all the conditions.
The next multiple of 240 is 240 + 7 + 240 = 487. This number also does not leave a remainder of 10 when divided by 15.
We continue this process until we find the smallest number that satisfies all the conditions. The correct answer is 235, which is the smallest multiple of 240 that leaves the desired remainders when divided by 12, 15, and 16.