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1. What is the least number of soldiers that can be drawn up in troops of 12, 15, 18 and 20 soldiers and also in form of a solid square?

A. 900

B. 400

C. 1600

D. 2500

Solution:

In this type of question, We need to find out the LCM of the given numbers.
LCM of 12, 15, 18 and 20;

\begin{aligned} 12 = 2 \times 2 \times 3; \\ 15 = 3 \times 5; \\ 18 = 2 \times 3 \times 3; \\ 20 = 2 \times 2 \times 5; \end{aligned}

Hence, LCM =

2 \times 2 \times 3 \times 5 \times 3

Since, the soldiers are in the form of a solid square.
Hence, LCM must be a perfect square. To make the LCM a perfect square, We have to multiply it by 5,
hence,
The required number of soldiers
=

2 \times 2 \times 3 \times 3 \times 5 \times 5

= 900

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