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u can make your own algorithms ... just see what u need to find & what methods u know ... make use of them calculating hcf will be easy ... just find common factors in both & for lcm=product of no.'s /hcf of no.'s
@Grey Coder: I think, your question is a very good one, and may I extend your question a little bit: Are there any good books ore websites, which do an introduction for non computer science people? Which information sources could you recommend?
To test whether a number is prime try every number from 2 to sqrt(n). If any of them divides n, n is not prime. Greatest common divisor can be found by Euclidean algorithm. gcd(a,b) is the same as gcd(a-b,b), when a>b. if a==b, you have found it LCM is a*b/gcd(a,b). Further you can look up binary search or some graph algorithms, like DFS.