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

The least number which when divided by $5, 6, 7$ and $8$ leaves $3$ as a remainder,but when divided by $9$ leaves no remainder,is:

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?

Find the greatest number of five digits which when divided by $12, 15, 21, 25$ and $28$ leaves $5, 8, 14, 18$ and $21$ as remainders, respectively.

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

In a school,$442$ boys and $374$ girls have been divided into the largest possible equal classes,so that each class of boys numbers the same as each class of girls. What is the number of classes?