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Three measuring rods are of lengths $120 \text{ cm}, 100 \text{ cm}$ and $150 \text{ cm}$. Find the least length of a fence that can be measured an exact number of times, using any of the rods. How many times each rod will be used to measure the length of the fence?
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$120 = 2^3 \times 3 \times 5, 100 = 2^2 \times 5^2, 150 = 2 \times 3 \times 5^2$ ($1\frac{1}{2}$ marks)
$LCM(120, 100, 150) = 2^3 \times 3 \times 5^2 = 600$ (1 mark)
$\therefore \text{Least length of the fence is } 600 \text{ cm.}$
$\text{Each rod is used 5, 6 and 4 times respectively}$ ($\frac{1}{2}$ mark)
$LCM(120, 100, 150) = 2^3 \times 3 \times 5^2 = 600$ (1 mark)
$\therefore \text{Least length of the fence is } 600 \text{ cm.}$
$\text{Each rod is used 5, 6 and 4 times respectively}$ ($\frac{1}{2}$ mark)