If a number is divisible by a given set of numbers, then that number is divisible by their LCM. 16=24 36=22×32 45=32×51 48=24×31 LCM of 16, 36, 45 and 48=24×32×51=720 The required number must be divisible by 720. The largest 4–digit number = 9999 Remainder of (

9999

720

)=639 The largest 4–digit number divisible by 720=9999−639=9360