The LCMSteps command accepts a list or sequence of integers, or an expression that contains %lcm, and gives steps for calculating the Least Common Multiple (or Lowest Common Multiple). It calculates these steps by prime factorization.

When expr is a list, one or more elements of the list can be given as a string. In this case, the string is parsed into an expression using InertForm:-Parse so that no automatic simplifications are applied, and thus no steps are missed.

The implicitmultiply option is only relevant when expr is a list of strings.  This option is passed directly on to the InertForm:-Parse command and will cause things like 2x to be interpreted as 2*x, but also, xyz to be interpreted as x*y*z.

The output and displaystyle options are described in Student:-Basics:-OutputStepsRecord. The return value is controlled by the output option.  

This function is part of the Student:-Basics package.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right)\:$

$\mathrm{LCMSteps}\left(\left[12\,3\,4\right]\right)$

$\begin{array}{lll}& & \mathrm{lcm}\left(12\,3\,4\right)\\ \text{•}& & \text{Prime factorize each term:}\\ & & \left[\begin{array}{c}12={\left(2\right)}^2\left(3\right)\\ 3=\left(3\right)\\ 4={\left(2\right)}^2\end{array}\right]\\ \text{•}& & \text{Take each factor of the highest power and multiply}\\ & & {\left(2\right)}^2\left(3\right)\\ \text{•}& & \text{Simplify}\\ & & 12\end{array}$

$\mathrm{LCMSteps}\left(4\,5\,6\right)$

$\begin{array}{lll}& & \mathrm{lcm}\left(4\,5\,6\right)\\ \text{•}& & \text{Prime factorize each term:}\\ & & \left[\begin{array}{c}4={\left(2\right)}^2\\ 5=\left(5\right)\\ 6=\left(2\right)\left(3\right)\end{array}\right]\\ \text{•}& & \text{Take each factor of the highest power and multiply}\\ & & {\left(2\right)}^2\left(3\right)\left(5\right)\\ \text{•}& & \text{Simplify}\\ & & 60\end{array}$

$\mathrm{LCMSteps}\left(''lcm(6,\; 8)\; +\; lcm(4,\; 5)\; -\; 5''\right)$

$\begin{array}{lll}& & \mathrm{lcm}\left(6\,8\right)+\mathrm{lcm}\left(4\,5\right)-5\\ \text{•}& & \text{Exmaine term}\\ & & \mathrm{lcm}\left(6\,8\right)\\ \text{•}& & \text{Prime factorize each term:}\\ & & \left[\begin{array}{c}6=\left(2\right)\left(3\right)\\ 8={\left(2\right)}^3\end{array}\right]\\ \text{•}& & \text{Take each factor of the highest power and multiply}\\ & & {\left(2\right)}^3\left(3\right)\\ \text{•}& & \text{Simplify}\\ & & 24\\ \text{•}& & \text{This gives:}\\ & & 24+\mathrm{lcm}\left(4\,5\right)-5\\ \text{•}& & \text{Exmaine term}\\ & & \mathrm{lcm}\left(4\,5\right)\\ \text{•}& & \text{Prime factorize each term:}\\ & & \left[\begin{array}{c}4={\left(2\right)}^2\\ 5=\left(5\right)\end{array}\right]\\ \text{•}& & \text{Take each factor of the highest power and multiply}\\ & & {\left(2\right)}^2\left(5\right)\\ \text{•}& & \text{Simplify}\\ & & 20\\ \text{•}& & \text{This gives:}\\ & & 24+20-5\\ \text{•}& & \text{Simplify}\\ & & 39\end{array}$

The Student:-Basics:-LCMSteps command was introduced in Maple 2024.

For more information on Maple 2024 changes, see Updates in Maple 2024.