Sheep

3.js

// 最大公约数
const gcd = (a, b) => a === 0 ? b : gcd(b % a, a)

// 最小公倍数
const lcm = arr => arr.reduce((a, b) => a * b / gcd(a, b), 1)

const overallTotal = 9 / 10
const overallAvg = overallTotal / 3

for (let x = 2; ; ++x) {
  if (1 / x <= overallAvg) break
  for (let y = x + 1; ; ++y) {
    if (1 / y <= (overallTotal - 1 / x) / 2) break
    for (let z = y + 1; ; ++z) {
      const m = lcm([x, y, z])
      const n = m - 1
      const total = n / m
      const avg = total / 3
      if (1 / x <= avg) break
      if (1 / y <= (total - 1 / x) / 2) break
      // important: z > n
      if (z > n && (1 / z < (total - 1 / x - 1 / y))) break

      if (m / x + m / y + m / z + 1 === m) {
        console.log(x, y, z, n)
      }
    }
  }
}