We have
"\\frac{x}{8200}+\\frac{y}{4300}=\\frac{43x+82y}{352600} \\\\ \\text{But the gcd(43x+82y,352600)} = \\frac{(43x+82y)352600}{lcm(43x+82y,352600)}, \\text{ then for every } x,y\\in \\mathbb{Z} \\text{ gcd(43x+82y,352600) divides (43x+82y) and 352600} \\\\ \\therefore \\boxed{\\text{ the lowest denominator is } \\frac{352600}{gcd(43x+82y,352600)}=\\frac{lcm(43x+82y,352600)}{43x+82y} } \\\\ \\text{For example if x=y=1 then we will have the lowest denominator to be } \\frac{lcm(43+82,352600)}{43+82}= \\frac{lcm(125,352600)}{125}=\\frac{1763000}{125}=14104"
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