**LCM (Least Common Multiple)**

In arithmetic and number theory, the **least common multiple**, **lowest common multiple**, or **smallest common multiple** of two integers *a* and *b*, usually denoted by **lcm(***a*, *b*), is the smallest positive integer that is divisible by both *a* and *b*. ^{}^{}^{}Since division of integers by zero is undefined, this definition has meaning only if *a* and *b* are both different from zero.^{} However, some authors define lcm(*a*,0) as 0 for all *a*, which is the result of taking the lcm to be the least upper bound in the lattice of divisibility.

The lcm is the "lowest common denominator" (lcd) that can be used before fractions can be added, subtracted or compared. The lcm of more than two integers is also well-defined: it is the smallest positive integer that is divisible by each of them.^{}

**HCF (Highest Common Factor)**

As the rules of mathematics dictate, the greatest common divisor or the gcd of two or more positive integers happens to be the largest positive integer that divides the numbers without leaving a remainder. For example, take 8 and 12. The H.C.F. of 8 and 12 will be 4 because the highest number that can divide both 8 and 12 is 4.