The greatest common divisor (gcd) of two integers a and b is the largest positive integer that divides both a and b without a remainder.
The gcd can be calculated using various methods such as the Euclidean algorithm or prime factorization.
The gcd and lcm are related by the following formula: lcm(a,b) = (a*b) / gcd(a,b). This means that the lcm is the product of the two numbers divided by their gcd.
The gcd is an important concept in number theory as it helps in solving various problems related to integers, such as finding the common factors of two numbers or determining whether two numbers are coprime (have a gcd of 1).
The gcd is used in various real life applications such as cryptography, where it is used to find a common key for secure communication. It is also used in simplifying fractions, finding the period of a repeating decimal, and in determining the best ratio for mixing ingredients in recipes.