The $H.C.F.$ of two numbers is $11$ and their $L.C.M.$ is $693$. If one of the numbers is $77$,find the other.

Find the largest number of four digits exactly divisible by $14, 24, 27$ and $32$.

The $HCF$ and $LCM$ of two numbers are $11$ and $385$ respectively. If one number lies between $75$ and $125,$ then that number is

Find the greatest number that will divide $390, 495,$ and $300$ without leaving a remainder.

The least perfect square number which is divisible by $3, 4, 5, 6$ and $8$ is:

Let $N$ be the least six-digit number which,when divided by $4, 6, 10,$ and $15,$ leaves the same remainder of $2$ in each case. The sum of the digits in $N$ is: