Documentation

# lcm

Least common multiple

## Syntax

``lcm(A)``
``lcm(A,B)``

## Description

example

````lcm(A)` finds the least common multiple of all elements of `A`.```

example

````lcm(A,B)` finds the least common multiple of `A` and `B`.```

## 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

collapse all

Input value, specified as a number, symbolic number, variable, expression, function, or a vector or matrix of numbers, symbolic numbers, variables, expressions, or functions.

Input value, specified as a number, symbolic number, variable, expression, function, or a vector or matrix of numbers, symbolic numbers, variables, expressions, or functions.

## 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.