a) 900
b) 400
c) 1600
d) 2500
Answer: a
Explanation: We need to find out the LCM of the given numbers.
LCM of 12, 15, 18 and 20;
$$\eqalign{
& 12 = 2 \times 2 \times 3; \cr
& 15 = 3 \times 5; \cr
& 18 = 2 \times 3 \times 3; \cr
& 20 = 2 \times 2 \times 5; \cr} $$
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,
The required number of soldiers
= $$2 \times 2 \times 3 \times 3 \times 5 \times 5$$
= 900
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