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 greatest number of five digits which when divided by $4, 6, 10$ and $15$ leaves the same remainder $3$ in each case.

If the $L.C.M.$ and $H.C.F.$ of two expressions are $(x^{2}+6x+8)(x+1)$ and $(x+1)$ respectively, and one of the expressions is $x^{2}+3x+2$, find the other.

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:

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 $m$)?

$A$ room is $4\, m\, 37\, cm$ long and $3\, m\, 23\, cm$ broad. It is required to pave the floor with minimum square slabs. Find the number of slabs required for this purpose.