Write an algorithm and draw a flowchart to find greatest common divisor and smallest common divisor of two given positive number.

Sure, here is the algorithm to find the greatest common divisor (GCD) and least common multiple (LCM) of two given positive numbers. Please note that the smallest common divisor of any two positive numbers is always 1, so we don't need to find that. The LCM is considered as the smallest common multiple, not divisor.

Algorithm:

1. Start
2. Input the two numbers, num1 and num2.
3. Set a variable gcd to 1.
4. For i from 1 to the minimum of num1 and num2,
   • If num1 and num2 are both divisible by i, set gcd to i.
5. Print gcd as the greatest common divisor.
6. Calculate lcm as (num1*num2)/gcd.
7. Print lcm as the least common multiple.
8. End

Flowchart:

1. Start
2. ↓
3. Input num1, num2
4. ↓
5. Initialize gcd = 1
6. ↓
7. For i = 1 to min(num1, num2)
8. ↓
9. Is num1 mod i == 0 and num2 mod i == 0?
10. ↓ Yes → Update gcd = i, No → Continue loop
11. ↓
12. End of loop
13. ↓
14. Print gcd
15. ↓
16. Calculate lcm = (num1*num2)/gcd
17. ↓
18. Print lcm
19. ↓
20. End

Please note that this is a simple algorithm and flowchart. There are more efficient algorithms available for finding GCD and LCM, such as the Euclidean algorithm.