### Instruction: What is the largest two-digit number that is divisible by both of its digits, and the digits are distinct?### Response: I want to find a two-digit number that is divisible by both of its digits, and the digits are different from each other.
To be divisible by both of its digits, the number must be a multiple of the product of the digits.
For example, 36 is divisible by both 3 and 6, and 3 * 6 = 18.
So I want to find the largest possible product of two distinct digits, and then the largest multiple of that product that is less than 100.
The largest possible product of two distinct digits is 9 * 8 = 72.
The largest multiple of 72 that is less than 100 is 72 itself.
So the largest two-digit number that is divisible by both of its digits, and the digits are distinct, is 72.