If Joelle multiplied 792 by a positive integer and came up with a perfect square as her answer, then what is the smallest integer she could have multiplied 792 by?

792 = 2^3 * 3^2 * 11. From factoring 792, it is quite obvious that: 2 x 11 =22 is the smallest positive integer, because: 792 x 2 x 11 =17,424 = 2^4 * 3^2 * 11^2 =which is the perfect square of 132.