The $LCM$ of two numbers is $1008$ and their $HCF$ is $36$. If one of the two numbers is $144$,find the other number.

The $LCM$ of two prime numbers $x$ and $y$ $(x > y)$ is $161$. Find the value of $(3y - x)$.

Find the least number which when divided by $16, 18, 20$ and $25$ leaves $4$ as a remainder in each case,but when divided by $7$ leaves no remainder.

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

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

Find the smallest whole number which is exactly divisible by $6, 8, 15, 18$ and $24$.