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

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

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

Three numbers which are co-prime to each other are such that the product of the first two is $551$ and that of the last two is $1073$. The sum of the three numbers is:

How many numbers are there from $300$ to $700$ which are divisible by $2, 3,$ and $7$?

The traffic lights at three different road crossings change after every $48\, seconds,$ $72\, seconds$ and $108\, seconds,$ respectively. If they all change simultaneously at $8: 20: 00$ $hours,$ then they will again change simultaneously at