Between two sets hackerrank solution with github code

**tutorial: how to solve "between two sets" problem on hackerrank**

the "between two sets" problem on hackerrank involves finding all integers that are factors of the elements of the second array and are multiples of the elements of the first array. in other words, you need to find the integers that are common multiples of all elements in the first array and factors of all elements in the second array.

here is a step-by-step guide to solving this problem:

1. **read input**: the first line of input contains two space-separated integers, n and m, representing the number of elements in arrays a and b, respectively. the next two lines contain the elements of arrays a and b.

2. **find the lcm of array a**: calculate the least common multiple (lcm) of all elements in array a. this can be done by iterating through the elements and finding the lcm of each pair of elements.

3. **find the gcd of array b**: calculate the greatest common divisor (gcd) of all elements in array b. this can be done by iterating through the elements and finding the gcd of each pair of elements.

4. **find the multiples of lcm**: find all multiples of the lcm obtained in step 2. these multiples will be potential candidates for the integers that are factors of array b and multiples of array a.

5. **check if each multiple is a factor of array b**: for each multiple obtained in step 4, check if it is a factor of all elements in array b by calculating the gcd of the multiple and each element in array b. if the gcd is equal to the element itself, then the multiple is a factor of that element.

6. **count the valid integers**: count the number of valid integers that satisfy the conditions and return the count as the final answer.

**github code example:**

**explanation:**
- in this code, we define functions to calculate the gcd and lcm of two numbers.
- we then calculate the lcm of array a and the gcd of array b.
- next, we iterate through the multiples of the lcm and check if they are factors of ...

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