$A$ number, when divided successively by $4, 5$ and $6$, leaves remainders $2, 3$ and $4$ respectively. The least such number is

Find the greatest number of four digits which is exactly divisible by $24, 28, 30$ and $35$.

Two pipes of length $1.5\, m$ and $1.2\, m$ are to be cut into equal pieces without leaving any extra length of pipes. The greatest length of the pipe pieces of same size which can be cut from these two lengths will be (in $metre$)

The $LCM$ of two numbers is $495$ and their $HCF$ is $5.$ If the sum of the numbers is $100,$ then their difference is

Find the greatest number which will divide $3962, 4085$ and $4167$ leaving the same remainder in each case.

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 $m$)