Definitions of GCD and LCM

The GCD and LCM group of functions includes the following three functions: • the greatest common divisor (gcd): • the least common multiple (lcm): • the extended greatest common divisor (egcd):

These functions are defined in the following ways:

is the greatest common divisor of the integers (or rational) . It is the greatest integer factor common to all the .

is the least common multiple of the integers (or rational) . It is the minimal positive integer that divides all the .

is the extended greatest common divisor of the integers . In particular,

Examples: The greatest common divisor of 21 and 48, is 3. Similar examples are , , . The least common multiple of the three numbers 2, 4, and 5, is . Similar examples are , , . The extended greatest common divisor of 21 and 48 is because the greatest common divisor and . Similarly, .