# 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

**Answer: Option A **

__Solution(By Examveda Team)__

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

$$\eqalign{ & 12 = 2 \times 2 \times 3; \cr & 15 = 3 \times 5; \cr & 18 = 2 \times 3 \times 3; \cr & 20 = 2 \times 2 \times 5; \cr} $$

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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Related Questions on Number System

**Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
**

A. 12, 24, 36

B. 11, 22, 33

C. 12, 24, 32

D. 5, 10, 15

why lcm multiply by 5 ?