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Question

# A perfect square is an integer that is the square of an integer. Suppose that m and n are positive integers, such that mn>15. If 15mn is a perfect square, calculate the least possible value of mn.

A
60
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B
80
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C
70
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D
40
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E
50
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Solution

## The correct option is B 60As given 15mn is a perfect square.So, √15mn to be an integer.√15mn=√5×3×m×nAssume m=3 , n=5⇒ √5×3×m×n=√52.32=15But it is mn<15.So, assume m =3×2 ; n=5×2⇒ √5.3×m×n=√5.3.3.2.5.2=√52.32.22=30 is an integer.As you can see that the least possible value of m and n are 6 and 10.Hence, option A is correct.

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