Question : What is that least perfect square, which is exactly divisible by each of 12, 84 and 24?
Option 1: 2304
Option 2: 7056
Option 3: 11664
Option 4: 1764
Correct Answer: 7056
Solution :
Let's find the correct least perfect square that is exactly divisible by each of 12, 84, and 24.
Prime factorization of 12 = ${2}^{2}×3$
Prime factorization of 84 = ${2}^{2}×3×7$
Prime factorization of 24 = ${2}^{3}×3$
Least Common Multiple = 2 × 2 × 2 × 3 × 7 = 168
⇒ Required perfect square = 168 × 2 × 3 × 7 = 7056
Hence, the correct answer is 7056.
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