Three-digit division remainder

Find the largest three-digit number that gives the remainder 1 when divided by three, gives the remainder 2 when divided by four, gives the remainder 3 when divided by five, and gives the remainder 4 when divided by six.

Final Answer:

x =  958

Step-by-step explanation:

$$\begin{gathered} 3...\text{ prime number} \\ 4=2^2 \\ 5...\text{ prime number} \\ 6=2\cdot 3 \\ LCM(3,4,5,6)=2^2\cdot 3\cdot 5=60 \\ y=LCM(3,4,5,6)=60 \\ {k}_1=999/y=999/60=\frac{333}{20}=16\frac{13}{20}=16.65 \\ {x}_1=15\cdot y=15\cdot 60=900 \\ {x}_2=x_1+y=900+60=960 \\ {x}_1<x<x_2 \\ 900<x<960 \\ x=958 \end{gathered}$$

Try another example