What is the smallest number which when increased by $3$ is divisible by $16, 24, 30$ and $32$?

Find the maximum possible length which can be used to measure exactly the lengths $6 \, m$,$4 \, m \, 75 \, cm$,and $10 \, m \, 25 \, cm$. (in $, cm$)

The product of two numbers is $6760$ and their $H.C.F.$ is $13.$ How many such pairs can be formed?

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

$A$ wholesale tea dealer has $408$ kilograms,$468$ kilograms,and $516$ kilograms of three different qualities of tea. He wants to pack all of it into boxes of equal size without mixing the different qualities. Find the capacity of the largest possible box.

Three different containers contain different quantities of a mixture of milk and water,measuring $403 \ kg$,$434 \ kg$,and $465 \ kg$. What is the largest measure that can measure all these quantities exactly? (in $kg$)