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Let f, g, h ∈ F[X] with h a greatest common divisor of f and g. Show that

(i) f /h and g/h are coprime,

(ii) fg/h is a least common multiple of f and g.

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    $\begingroup$ Do you know how to prove this for integers instead of polynomials? The proof is deceptively similar. $\endgroup$ – Arthur Nov 13 '19 at 18:55
  • $\begingroup$ I know how to for the first part $\endgroup$ – user720013 Nov 13 '19 at 19:05