Find the least number of soldiers in a regiment such that they stand in rows of 15, 20, 25 and
form a perfect square. Use prime factorization method
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Ans:- 300
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Given data: 15, 20 and 25
To find: Perfect square using prime factorization method
Solution:
First we need to find the LCM of the given three numbers.
15 = 5 × 3
20 = 5 × 4
25 = 5 × 5
The LCM of (15, 20, 25) = 5 × 3 × 4 × 5 = 300.
Now to find the perfect square we need to take LCM of 300.
300 = 5 × 5 × 3 × 2 × 2
The Least number is 3. So, we need to multiple the LCM of (15, 20, 25) by 3 (300 × 3 = 900).
Hence the perfect square using prime factorization method is 900.
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