Find the least number which when decreased by $11$ is divisible by $14, 15, 21, 32$ and $60$.

The greatest number that divides $411, 684,$ and $821$ and leaves $3, 4,$ and $5$ as remainders,respectively,is

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 $metre$)

Three numbers are in the ratio $3: 4: 5$ and their $LCM$ is $2400$. Their $HCF$ is

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:

Find the least number which is a multiple of $31$ and when divided by $15, 24$ and $32$ leaves the remainders $2, 11$ and $19$,respectively.