[Vlasenko Fedor]

let str = 'kabc5 sabc0 abjcde abcfg fgabcfg2 safds abc'
let arr = str.split(/\s+/)
let res = 1
const find = arr => {
  let temp = {}
  arr.forEach(v => {
    let key = v.substr(0, res)
    temp[key] = (temp[key] >>> 0) + 1
  })
  arr = arr.filter(v => temp[v.substr(0, res)] > 1)
  if (arr.length) {
    res += 1
    find(arr)
  }
}

find(arr)
console.log(res)

мой вариант решения