Dr. Lal and Jain Solutions for Exercise 1: Exercise 8

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

Find the least number divisible by $4, 6, 8, 20$, and it must be a perfect square also.

Find the least number which when divided by $8$, $12$ and $16$ leaves $3$ as remainder in each case, but when divided by $7$, leaves no remainder:

Find the greatest weight which can be contained exactly in $1$ kg $235$ gm and $3$ kg $430$ gm.

The LCM of two numbers is $2079$ and their HCF is $27$. If one of the numbers is $189$, find the other.

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

There are four numbers. The HCF of each pair is $3$ and the LCM of all the $4$ numbers is $116$. What is the product of $4$ numbers?

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?