Multiple choice general knowledge math & puzzles

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

  1. 900

  2. 1200

  3. 2500

  4. 3600
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D Correct answer
Explanation

LCM of 3,4,5,6,8 = 2^3 × 3 × 5 = 120. For a perfect square, all prime exponents must be even. Multiply by 2 × 3 × 5 = 30 to get 3600.

AI explanation

The LCM of 3, 4, 5, 6, and 8 is 120 = 2³×3×5. For a number to be a perfect square, every prime factor must appear to an even power, so 2³ needs one more factor of 2, and 3¹ and 5¹ each need one more factor of themselves: multiplying 120 by 2×3×5=30 gives 3600 = 60², the smallest perfect square divisible by all five numbers.

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