In a school,$442$ boys and $374$ 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?

Find the sum of the numbers between $500$ and $700$ such that when they are divided by $6, 8$ and $12$ it leaves no remainder.

The traffic lights at three different road crossings change after every $48\, seconds,$ $72\, seconds$ and $108\, seconds,$ respectively. If they all change simultaneously at $8: 20: 00$ $hours,$ then they will again change simultaneously at

$L.C.M.$ 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

Three pieces of timber $42 \ m$,$49 \ m$,and $63 \ m$ long have to be divided into planks of the same length. What is the greatest possible length of each plank (in $m$)?

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