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

Find the greatest number that will divide $964, 1238$ and $1400$ leaving remainders $41, 31$ and $51$ respectively.

The $HCF$ of two numbers is $8$. Which one of the following can never be their $LCM$?

Three men start together to travel the same way around a circular track of $11 \text{ km}$ in circumference. Their speeds are $4 \text{ km/h}$,$5.5 \text{ km/h}$,and $8 \text{ km/h}$ respectively. When will they meet at the starting point? (in hours)

The $H.C.F.$ and $L.C.M.$ of two numbers are $8$ and $48,$ respectively. If one of the numbers is $24,$ then the other number is

The least multiple of $7,$ which leaves a remainder of $4,$ when divided by $6, 9, 15,$ and $18$ is