Determine the $L.C.M.$ of $\frac{2}{5}, \frac{3}{10}$ and $\frac{6}{25}$.

The traffic lights at three different road crossings change after $24$ seconds,$36$ seconds,and $54$ seconds,respectively. If they all change simultaneously at $10:15:00$ am,then at what time will they again change simultaneously?

Two numbers,both greater than $29$,have $HCF$ $29$ and $LCM$ $4147$. The sum of the numbers is

Find the least number which when divided by $2, 3, 4, 5$ and $6$ leaves $1, 2, 3, 4$ and $5$ as remainders,respectively,but when divided by $7$ leaves no remainder.

The $HCF$ of two numbers is $11$ and their $LCM$ is $7700.$ If one of the numbers is $275,$ then the other is:

Three bells ring together and they will ring at intervals of $6$ seconds,$7$ seconds and $8$ seconds respectively. After what interval will they again ring together? (in seconds)