Problem:
A and b are two positive integers such that the least prime factor of a is 3 and the least prime factor of b is 5. Calculate the least prime factor of (a b).

Solution:
To find the least prime factor of (a b), we need to understand the prime factorization of a and b.

Prime Factorization of a:
The least prime factor of a is 3. Therefore, we can write a as the product of its prime factors as follows:
a = 3 * p1 * p2 * ...
where p1, p2, ... are prime numbers greater than or equal to 3.

Prime Factorization of b:
The least prime factor of b is 5. Therefore, we can write b as the product of its prime factors as follows:
b = 5 * q1 * q2 * ...
where q1, q2, ... are prime numbers greater than or equal to 5.

Prime Factorization of (a b):
Now, let's calculate the prime factorization of (a b) by multiplying a and b:
(a b) = (3 * p1 * p2 * ...) * (5 * q1 * q2 * ...)
= 3 * 5 * p1 * p2 * q1 * q2 * ...

The least prime factor of (a b) is the smallest prime number that divides (a b) without leaving a remainder. From the prime factorization above, we can see that the least prime factor of (a b) is 3 * 5 = 15.

Therefore, the least prime factor of (a b) is 15.

Summary:
- The least prime factor of a is 3 and the least prime factor of b is 5.
- The prime factorization of a is a = 3 * p1 * p2 * ...
- The prime factorization of b is b = 5 * q1 * q2 * ...
- The prime factorization of (a b) is (a b) = 3 * 5 * p1 * p2 * q1 * q2 * ...
- Therefore, the least prime factor of (a b) is 15.