Problem: if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ?
Rationale: ( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) has one appearance of 3 ( in the 6 ) and no appearances of 5 . thus n must include at least 3 ^ 2 * 5 ^ 2 = 9 * 25 = 225 the answer is e .
annotated_formula: add(add(add(add(add(multiply(multiply(5, 7), 2), multiply(multiply(5, 7), 2)), multiply(multiply(5, 7), 2)), 7), const_4), const_4)