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

If $A$ and $B$ are the $H.C.F.$ and $L.C.M.$ respectively of two algebraic expressions $x$ and $y,$ and $A+B = x+y,$ then the value of $A^{3}+B^{3}$ is

Find the greatest number of four digits which must be added to $5231$ so that the final number becomes exactly divisible by $12, 15, 27, 32$ and $40$.

The traffic lights at three different road crossings change after $24$ seconds,$36$ seconds,and $54$ seconds,respectively. If they all change simultaneously at $10:15:00$ am,then at what time will they again change simultaneously?

The areas of three fields are $165 \ m^2$,$195 \ m^2$,and $85 \ m^2$ respectively. In each of the fields,a flower bed of equal length has to be made. If the flower bed in each of the fields is $3 \ m$ wide,then what is the maximum length of the flower bed in each of the fields? (in $m$)

The $LCM$ of two numbers is $1008$ and their $HCF$ is $36$. If one of the two numbers is $144$,find the other number.