lcm(a,b) = (a*b)/gcd(a,b)

[compsystems]

Hi, BP,

at XCAS
lcm(a,b) ↲ a*b

and the books

lcm(a, b) = (a*b)/gcd(a, b)

Why?

[parisse]

lcm(a,b) does not return a*b.
Try lcm(6,4) for example

[compsystems]

numerically if it returns the correct value, symbolically not.

assume(a, symbol):; assume(b, symbol):; [↲]
gcd(a, b) [↲] 1 ↦ (a* b)/lcm(a, b)

[parisse]

a and b are considered as polynomials, since they are prime together lcm(a,b) is a*b.

[compsystems]

ok ^

lcm(a*x^0,b*x^0) [↲] a*b

but, you can add a new rule, if the user defines the following

assume(a,integer);additionally(a>0); assume(b,integer);additionally(b>0);
lcm(a,b) [↲] '(a* b)/gcd(a, b)'

Just remember the "formula" of this function. similarly to
abs(a+b*i) [↲] sqrt(a^2+b^2)
unitV(a+b*i) [↲] (a+b*i)/(sqrt(a^2+b^2))

[parisse]

a and b are considered as multivariate polynomials (with respect to variables [a,b]).
There is no "rule" in lcm, lcm is a polynomial instruction (like gcd).