### Instruction: A number $x$ is equal to $7\cdot24\cdot48$. What is the smallest positive integer $y$ such that the product $xy$ is a perfect cube? Let's write a program.### Response: import sympy as sp

# define the number x
x = 7*24*48

# get the prime factorization of x
factors = sp.factorint(x)

# for xy to be a perfect cube, all exponents in the prime factorization of x must be multiples of 3
# if not, we multiply by the missing factors to make them multiples of 3

y = 1
for factor, exponent in factors.items():
    if exponent % 3 != 0:
        # multiply y by the factor to the power of the missing exponents
        y *= factor**(3 - exponent % 3)

print(y)