# Problem of the Week Problem D Digits Multiplied

The digits of any positive integer can be multiplied together to give the digit product for the integer. For example, $$345$$ has the digit product of $$3 \times 4 \times 5 = 60$$. There are many other positive integers that have $$60$$ as a digit product. For example, $$2532$$ and $$14\,153$$ both have a digit product of $$60$$. Note that $$256$$ is the smallest positive integer with a digit product of $$60$$.

There are also many positive integers that have a digit product of $$2160$$. Determine the smallest such integer.