{"problem":{"name":"Factorial and Multiple","description":{"content":"You are given an integer $K$ greater than or equal to $2$.   Find the minimum positive integer $N$ such that $N!$ is a multiple of $K$. Here, $N!$ denotes the factorial of $N$. Under the Constraints o","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc280_d"},"statements":[{"statement_type":"Markdown","content":"You are given an integer $K$ greater than or equal to $2$.  \nFind the minimum positive integer $N$ such that $N!$ is a multiple of $K$.\nHere, $N!$ denotes the factorial of $N$. Under the Constraints of this problem, we can prove that such an $N$ always exists.\n\n## Constraints\n\n*   $2\\leq K\\leq 10^{12}$\n*   $K$ is an integer.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc280_d","tags":[],"sample_group":[["30","5\n\n*   $1!=1$\n*   $2!=2\\times 1=2$\n*   $3!=3\\times 2\\times 1=6$\n*   $4!=4\\times 3\\times 2\\times 1=24$\n*   $5!=5\\times 4\\times 3\\times 2\\times 1=120$\n\nTherefore, $5$ is the minimum positive integer $N$ such that $N!$ is a multiple of $30$. Thus, $5$ should be printed."],["123456789011","123456789011"],["280","7"]],"created_at":"2026-03-03 11:01:14"}}