LCM (G Dataflow)

Version:
Last Modified: January 9, 2017

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