The greatest number that must be taken out from $999$ such that the resulting number may be divisible by $10, 15,$ and $18$ is—

What is the smallest positive number, which when divided by $3,4$ and $5$ will have a remainder of $2$?

Find the least number which when divided by $8,9,12$ and $15$ leaves the remainder $1$.

Traffic light at one particular crossing changes after every $40$ seconds. The traffic light at the next crossing changes after every $32$ seconds. At a certain time they change together. After what time will they again change together?

The LCM of two numbers is $280$ and their HCF is $7$. One of the numbers is $35$. Find the other number.

Find the least number which, upon being divided by $2, 3, 4, 5$ and $6$ leaves in each case a remainder of $1$.

A merchant has three kinds of wine, of the first kind $403$ gallons, of the second $527$ gallons and of the third $589$ gallons. What is the least number of full casks of equal size in which this can be stored without mixing?