### Instruction: The least common multiple of two integers is 240, and the greatest common divisor is 24. Given that one of the integers is 48, what is the other integer?### Response: I know that the least common multiple of two integers is the smallest positive number that is a multiple of both integers, and the greatest common divisor is the largest positive number that is a factor of both integers.
I also know that there is a formula that relates the least common multiple, the greatest common divisor, and the two integers: LCM(a, b) = a * b / GCD(a, b).
So, if I let a = 48 and b = the other integer, I can plug them into the formula and get: 240 = 48 * b / 24.
To solve for b, I can multiply both sides by 24 and get: 240 * 24 = 48 * b.
Then, I can divide both sides by 48 and get: 240 * 24 / 48 = b.
Finally, I can simplify this expression and get: b = 120.
So, the other integer is 120.