Answer:
359
Explanation:
the prime factors of the numbers are
18 = 2×3×3
20 = 2×2×5
24 = 2×2×2×3
the lowest common multiple is therefore
2×2×2×3×3×5 = 360
the difference between the checked divisor numbers and the expected remainder is constantly 1 :
18 - 17 = 1
20 - 19 = 1
24 - 23 = 1
so, we can deduct this constant 1 from the LCM and get the desired number :
360 - 1 = 359
verify :
359 ÷ 18 = 19 remainder 17
359 ÷ 20 = 17 remainder 19
359 ÷ 24 = 14 remainder 23