A property of cyclotomic polynomials

Given two cyclotomic polynomials ${\mathrm{\Phi }}_n(x)$ and ${\mathrm{\Phi }}_m(x)$, $n≠m$, we determine the minimal natural number k such that we can write $$k=a(x){\mathrm{\Phi }}_n(x)+b(x){\mathrm{\Phi }}_m(x),$$ with a(x) and b(x) integer polynomials.