$3=60^\frac{k}{x}$
$4=60^\frac{k}{y}$
$5=60^\frac{k}{z}$
$3x4x5=60^{k(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})}$
$60^1=60^{k(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})}$
$1=k(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})$
$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{k}$
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