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1. Three numbers are in the ratio 2 : 3 : 4, If their LCM is 240 the smaller of the three numbers is = ?

A. 20

B. 60

C. 30

D. 80

Solution:

\begin{aligned} Let number are \\ = 2 x, 3 x, 4 x \\ given, \\ LCM of (2 \times 3 \times 4) x = 24 x \\ 24 x = 240 \\ x = 10 \\ ∴ numbers are 2 \times 10 =  20 \\ 3 \times 10 = 30 \\ 4 \times 10 = 40 \\ ∴ Smaller is 20 \end{aligned}

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