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I do not know how to code the following.

Suppose you have a list lst={x1,...,xn}and you need to find a number $Z$, to a given digits precision such that

Z * lst={y1,..,yn}

in which all $y_i$ are integers. I am clueless.

Thanks in advance.

Edit: Also, I would like $Z$ to be the minimum positive real such that this is true.

I do not know how to code the following.

Suppose you have a list lst={x1,...,xn}and you need to find a number $Z$, to a given digits precision such that

Z * lst={y1,..,yn}

in which all $y_i$ are integers. I am clueless.

Thanks in advance.

Edit: To be more precise, given a list of numbers lst={x1,...,xn}and a parameter $\varepsilon>0 $ I want to find the smallest real number $Z$ such that for each $i \leq n$ we have $\mid Z\cdot x_i-\text{Round}(z\cdot x_i) \mid<\varepsilon $. Here Round$(x)$ denotes the closest integer to $x$.

I do not know how to code the following.

Suppose you have a list lst={x1,...,xn}and you need to find a number $Z$, to a given digits precision such that

Z * lst={y1,..,yn}

in which all $y_i$ are integers. I am clueless.

Thanks in advance.

Edit: Also, I would like $Z$ to be the minimum positive integer such that this is true.

I do not know how to code the following.

Suppose you have a list lst={x1,...,xn}and you need to find a number $Z$, to a given digits precision such that

Z * lst={y1,..,yn}

in which all $y_i$ are integers. I am clueless.

Thanks in advance.

Edit: Also, I would like $Z$ to be the minimum positive real such that this is true.

I do not know how to code the following.

Suppose you have a list lst={x1,...,xn}and you need to find a number $Z$, to a given digits precision such that

Z * lst={y1,..,yn}

in which all $y_i$ are integers. I am clueless.

Thanks in advance.

I do not know how to code the following.

Suppose you have a list lst={x1,...,xn}and you need to find a number $Z$, to a given digits precision such that

Z * lst={y1,..,yn}

in which all $y_i$ are integers. I am clueless.

Thanks in advance.

Edit: Also, I would like $Z$ to be the minimum positive integer such that this is true.