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Two numbers are in the ratio $3 : 5$ and their LCM is $180$. Find the HCF of these two numbers.
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Let the numbers be $3x$ and $5x$. HCF = $x$ ($\frac{1}{2}$ Mark)
HCF $\times$ LCM = Product of two numbers ($\frac{1}{2}$ Mark)
$x \times 180 = 3x \times 5x$ (1 Mark)
$x = 12$ ($\frac{1}{2}$ Mark)
HCF of numbers is $12$. ($\frac{1}{2}$ Mark)
HCF $\times$ LCM = Product of two numbers ($\frac{1}{2}$ Mark)
$x \times 180 = 3x \times 5x$ (1 Mark)
$x = 12$ ($\frac{1}{2}$ Mark)
HCF of numbers is $12$. ($\frac{1}{2}$ Mark)