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1. The HCF and LCM of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is = ?

A. 12

B. 48

C. 84

D. 108

Solution:

\begin{aligned} Let the numbers be x and 4 x \\ Then , x \times 4 x = 84 \times 21 \\ \Leftrightarrow x^{2} = (\frac{84 \times 21}{4}) \\ \Leftrightarrow x = 21 \\ Hence larger number \\ =  4 x \\ = 84 \end{aligned}

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