Least common multiple

The least common multiple of two integers is the smallest positive integer between all the multiples of both. It is usually written as LCM(a, b). Likewise, the LCM of more than two integers is the smallest positive integer that is divisible by each of them.
Overview
Elementary arithmetic
In elementary arithmetic, the LCM is also the "lowest common denominator" (LCD) that must be calculated, before fractions can be added, subtracted or compared.

A multiple of a number is the product of that number and an integer. For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2. By the same principle, 10 is the least common multiple of 5 and 2 as well.

Relations with the greatest common divisor
It is known that:

where  is the greatest common divisor of a and b, This formula is often used to compute the LCD, by first finding the GCD of a and b.

Related pages
 Scalar
 Algebra
 Arithmetic
 Pure mathematics
 Mathematical analysis
 Greatest common divisor (GCD)

 References 

Category:Arithmetics
Category:Number theory