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Applications of LCM

I have 20 ora...

Question

I have 20 oranges. What is the least number of oranges I need to take such that I can divide the oranges into groups of 6 or groups of 9 without leftovers?

A

12

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B

15

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C

18

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D

9

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Solution

The correct option is C 18
To find the least number of oranges I must find the LCM of the given numbers 6 and 9.

$\begin{matrix} 3 & 6, 9 2, 3 \end{matrix}$

Since there are no common factors for 2 and 3 we cannot factorise it further.

Hence, the LCM of 6 and 9
= 3 × 2 × 3 = 18

We can pick a total of 18 oranges to divide them in groups of either 6 or 9 without leftovers.

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