If the product of two positive integers is 363, and the least common multiple of them is 33, what is the sum of the two positive integers?
To find the sum of the two positive integers, we need to determine what those integers are. Let's call the two integers "x" and "y".
We are given that the product of the two positive integers is 363, so we have the equation:
x * y = 363
We are also given that the least common multiple (LCM) of the two integers is 33. The LCM of two numbers is the smallest multiple that both numbers can divide evenly into. From this information, we can set up another equation:
LCM(x, y) = 33
Since we know the product of the two integers and their LCM, we can solve for x and y by finding their prime factorization and matching the factors accordingly.
The prime factorization of 363 is 3 * 11 * 11.
The prime factorization of 33 is 3 * 11.
From this, we can see that one of the integers must be 3 * 11 * 11 = 363 and the other integer must be 3, since the prime factor of 33 is 3.
Therefore, the two positive integers are 3 and 121 (or vice versa).
Now we can find the sum of these two integers:
3 + 121 = 124
So, the sum of the two positive integers is 124.