# Mathematical Algorithms | GCD & LCM

### Greatest Common Divisor (GCD):

The GCD of two numbers is defined as the largest integer that divides both integers without any remainder. It is also termed as the HCF (Highest Common Factor).

GCD of an array is the integer that divides all the elements of the array without leaving any remainder.

GCD of two numbers may be calculated using the following ways:

• Prime Factorization
• Divisions by Prime
• Euclidean Algorithm

### Least Common Multiple (LCM):

The LCM of two numbers is defined as the smallest integer which is a multiple of both integers.

LCM of an array is the smallest possible integer that is multiple of all the elements of the array.

Below are some process to find LCm of two numbers:

• Prime Factorization
• Divisions by Prime
• Using the relation between GCD and LCM

### Relation between GCD and LCM:

Consider two integers a and b and their GCD be gcd(a, b) and LCM be lcm(a, b). Therefore,

a * b = gcd(a, b) * lcm(a, b)

Some practice problems on GCD and LCM: Quick Links:

• Last Updated : 26 Sep, 2023