Final answer:
To find the least number that gives a remainder of 31 when divided by 32 and a remainder of 23 when divided by 32, the common multiple of 31 and 23 is 713. Therefore, the least number that satisfies the given conditions is 713.
Step-by-step explanation:
To find the least number that gives a remainder of 31 when divided by 32 and a remainder of 23 when divided by 32, we can start with the two given remainders and find their common multiple. In this case, the common multiple of 31 and 23 is 713. So, the least number that satisfies the given conditions is 713.