The least perfect square number which is divisible by 3, 4, 5, 6 and 8 is

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RRB GG Exam (Bhopal) 2008 click here to view all questions

The least perfect square number which is divisible by 3, 4, 5, 6 and 8 is

A900

B1600

C2500

D3600

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correct answer is: 3600 Explanation: To find the least perfect square divisible by 3, 4, 5, 6, and 8, we first determine the least common multiple (LCM) of these numbers. The prime factorizations are: - 3 = $3^1$ - 4 = $2^2$ - 5 = $5^1$ - 6 = $2^1 \times 3^1$ - 8 = $2^3$ The LCM is obtained by taking the highest powers of all primes: - $2^3$ - $3^1$ - $5^1$ Thus, LCM = $2^3 \times 3^1 \times 5^1 = 120$. To make this a perfect square, all exponents in its prime factorization must be even. Therefore, we multiply by $2^1 \times 3^1 \times 5^1$ to get: - $2^4 \times 3^2 \times 5^2 = 3600$. This is the smallest perfect square divisible by all the given numbers. Option a (900): Not divisible by 8 ($2^3$). Option b (1600): Not divisible by 3 or 6. Option c (2500): Not divisible by 3, 6, or 8. Option d (3600): Divisible by all and is a perfect square.   Akhilesh ? answered Mar 18 '25 at 22:52

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