Find the greatest number which will divide $2112$ and $2792$ leaving the remainder $4$ in each case.

Find the greatest number of four digits which when divided by $10, 15, 21$ and $28$ leaves $4, 9, 15$ and $22$ as remainders,respectively.

In a school,$391$ boys and $323$ girls have been divided into the largest possible equal classes,so that each class of boys numbers the same as each class of girls. What is the number of classes?

What is the smallest number which when increased by $3$ is divisible by $16, 24, 30$ and $32$?

Three bells ring together and they will ring at intervals of $6$ seconds,$7$ seconds and $8$ seconds respectively. After what interval will they again ring together? (in seconds)

$L.C.M.$ and $H.C.F.$ of two numbers $x$ and $y$ are $315$ and $3,$ respectively. If $x+y=36,$ the value of $\frac{1}{x}+\frac{1}{y}$ is