# LCM (G Dataflow)

Version:

Computes the least common multiple of the input values.

An integer.

An integer.

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## LCM(x, y)

Least common multiple of x and y.

## error out

Error information. The node produces this output according to standard error behavior.

## Algorithm for Computing the Least Common Multiple

LCM(x,y) is the smallest integer m for which there exist integers c and d such that

$x×c=y×d=m$

To compute LCM(x,y), consider the prime factorizations of x and y:

$x=\underset{i}{\prod }{{p}_{i}}^{{a}_{i}}$
$y=\underset{i}{\prod }{{p}_{i}}^{{b}_{i}}$

where pi are all the prime factors of x and y. If pi does not occur in a factorization, the corresponding exponent is 0. LCM(x,y) then is given by:

$\mathrm{LCM}\left(x,y\right)=\underset{i}{\prod }{{p}_{i}}^{\mathrm{max}\left({a}_{i},{b}_{i}\right)}$

The prime factorizations of 12 and 30 are given by:

$12={2}^{2}×{3}^{1}×{5}^{0}$
$30={2}^{1}×{3}^{1}×{5}^{1}$

so

$\mathrm{LCM}\left(12,30\right)={2}^{2}×{3}^{1}×{5}^{1}=60$

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported