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?

Three electronic devices make a beep after every $48\, seconds$,$72\, seconds$,and $108\, seconds$ respectively. They beeped together at $10:00\, a.m.$ The time when they will next make a beep together at the earliest is:

Find the least number which is a multiple of $31$ and when divided by $15, 24$ and $32$ leaves the remainders $2, 11$ and $19$,respectively.

If the sum of two numbers is $55$ and the $HCF$ and $LCM$ of these numbers are $5$ and $120$ respectively,then the sum of the reciprocals of the numbers is equal to

$L.C.M.$ 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

Is it possible to divide $1,000$ into two parts such that their $HCF$ is $15$?