What is the largest five-digit number that is exactly divisible by 32, 36, 40, 42, and 48?

Explanation

First, find the least common multiple (LCM) of the numbers 32, 36, 40, 42, and 48, which is 10080. To find the greatest five-digit number divisible by all these, divide the largest five-digit number, 99999, by 10080. The quotient is 9, and multiplying 10080 by 9 gives 90720. Therefore, 90720 is the highest five-digit number divisible by all the given numbers.