# lcm

Least common multiple

## Description

## Examples

### Least Common Multiple of Four Integers

To find the least common multiple of three or more values, specify those values as a symbolic vector or matrix.

Find the least common multiple of these four integers, specified as elements of a symbolic vector.

A = sym([4420, -128, 8984, -488]) lcm(A)

A = [ 4420, -128, 8984, -488] ans = 9689064320

Alternatively, specify these values as elements of a symbolic matrix.

A = sym([4420, -128; 8984, -488]) lcm(A)

A = [ 4420, -128] [ 8984, -488] ans = 9689064320

### Least Common Multiple of Rational Numbers

`lcm`

lets you find the least common
multiple of symbolic rational numbers.

Find the least common multiple of these rational numbers, specified as elements of a symbolic vector.

lcm(sym([3/4, 7/3, 11/2, 12/3, 33/4]))

ans = 924

### Least Common Multiple of Complex Numbers

`lcm`

lets you find the least common
multiple of symbolic complex numbers.

Find the least common multiple of these complex numbers, specified as elements of a symbolic vector.

lcm(sym([10 - 5*i, 20 - 10*i, 30 - 15*i]))

ans = - 60 + 30i

### Least Common Multiple of Elements of Matrices

For vectors and matrices, `lcm`

finds the
least common multiples element-wise. Nonscalar arguments must be the same
size.

Find the least common multiples for the elements of these two matrices.

A = sym([309, 186; 486, 224]); B = sym([558, 444; 1024, 1984]); lcm(A,B)

ans = [ 57474, 13764] [ 248832, 13888]

Find the least common multiples for the elements of matrix `A`

and the value `99`

. Here, `lcm`

expands
`99`

into the `2`

-by-`2`

matrix with all elements equal to `99`

.

lcm(A,99)

ans = [ 10197, 6138] [ 5346, 22176]

### Least Common Multiple of Polynomials

Find the least common multiple of univariate and multivariate polynomials.

Find the least common multiple of these univariate polynomials.

syms x lcm(x^3 - 3*x^2 + 3*x - 1, x^2 - 5*x + 4)

ans = (x - 4)*(x^3 - 3*x^2 + 3*x - 1)

Find the least common multiple of these multivariate polynomials. Because there are more than two polynomials, specify them as elements of a symbolic vector.

syms x y lcm([x^2*y + x^3, (x + y)^2, x^2 + x*y^2 + x*y + x + y^3 + y])

ans = (x^3 + y*x^2)*(x^2 + x*y^2 + x*y + x + y^3 + y)

## Input Arguments

## Tips

Calling

`lcm`

for numbers that are not symbolic objects invokes the MATLAB^{®}`lcm`

function.The MATLAB

`lcm`

function does not accept rational or complex arguments. To find the least common multiple of rational or complex numbers, convert these numbers to symbolic objects by using`sym`

, and then use`lcm`

.Nonscalar arguments must have the same size. If one input arguments is nonscalar, then

`lcm`

expands the scalar into a vector or matrix of the same size as the nonscalar argument, with all elements equal to the corresponding scalar.

## Version History

**Introduced in R2014b**