LCM and HCF Questions for Competitive Exams

A number which when divided by 10 leaves remainder of 9, when divided by 9 leaves a remainder of 8, and when divided by 8 leaves a remainder of 7, is: 

There are 24 peaches, 36 apricots and 60 bananas and they have to be arranged in several rows in such a way that every row contains the same number of fruits of only one type. What is the minimum number of rows required for this to happen? 

The smallest number, which when increased by 5 is divisible by each of 24, 32, 36 and 54, is 

If the students of a class can be grouped exactly into 6 or 8 or 10, then the minimum number of students in the class must be. 

A fraction becomes $${1\over 6}$$ when 4 is subtracted from its numerator and 1 is added to its denominator. If 2 and 1 are respectively added to its numerator and the denominator, it becomes $${1\over 3}$$. Then, the LCM of the numerator and denominator of the fraction, must be 

What least number must be subtracted from 1936 so that the resulting number when divided by 9, 10 and 15 will leave in each case the same remainder 7? 

The least number, which when divided by 4, 5 and 6 leaves remainder 1, 2 and 3 respectively is:

A farmer has 945 cows and 2475 sheep. He farms them into flocks, keeping cows and sheep separate and having the same number of animals in each flock. If these flocks are as large as possible, then the maximum number of animals in each flock and total number of flocks required for the purpose are respectively 

The product of the LCM and HCF of two numbers is 24. The difference of the two numbers is 2. Find the numbers? 

A milkman has 75 litres milk in one cane and 45 litres in another. The maximum capacity of container which can measure milk of either container exact number: