Least common multiple of polynomials

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lcm(p, q, …)
lcm(f, g, …)


lcm(p, q, ...) calculates the least common multiple of any number of polynomials. The coefficient ring of the polynomials may either be the integers or the rational numbers, Expr, a residue class ring IntMod(n) with a prime number n, or a domain.

All polynomials must have the same indeterminates and the same coefficient ring.

Polynomial expressions are converted to polynomials. See poly for details. FAIL is returned if an argument cannot be converted to a polynomial.

The return value is of the same type as the input polynomials, i.e., either a polynomial of type DOM_POLY or a polynomial expression.

lcm returns 1 if all arguments are 1 or - 1, or if no argument is given. If at least one of the arguments is 0, then lcm returns 0.

Use ilcm if all arguments are known to be integers, since it is much faster than lcm.


Example 1

The least common multiple of two polynomial expressions can be computed as follows:

lcm(x^3 - y^3, x^2 - y^2);

One may also choose polynomials as arguments:

p := poly(x^2 - y^2, [x, y], IntMod(17)):
q := poly(x^2 - 2*x*y + y^2, [x, y], IntMod(17)):
lcm(p, q)

delete f, g, p, q:


pq, …

polynomials of type DOM_POLY

fg, …

polynomial expressions

Return Values

Polynomial, a polynomial expression, or the value FAIL.

Overloaded By

f, g, p, q

See Also

MuPAD Functions