Two numbers are in the ratio $4 : 5$ and their L.C.M. is $180.$ Find the smaller number.

8

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15

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36

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45

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Solution

The correct option is B $36$
Let the numbers be $4 x$ and $5 x$
Now L.C.M of $4 x$ and $5 x = 4 \times 5 \times x = 20 x$
Given, $20 x = 180 \Rightarrow x = 9$
$∴$ Smaller number $= 4$ $\times$ $9 = 36$

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