CT 14: LCM & HCF – III

1.The largest number which will divide the numbers 4743, 7497, and 8721 leaving the same remainder in each case will be?

2. If three positive numbers are in the ratio 2 : 3 : 5 whose L.C.M. is 2400, then find the H.C.F. of the three numbers.

3. The number of students in grades 10, 11 and 12 of a school are 348, 256 and 480 respectively. All students were divided into different groups, with no group having students from more than one grade. What is the minimum number of groups that would be formed if all the groups have the same number of students?

4. The HCF of two numbers is 8 and the product of the two numbers is 6400. How many pairs of numbers exist, which satisfy the above conditions?

5. Find the value of the least 4-digit positive valued integer N on which dividing by the numbers 7, 11 and 13 it will give remainder as 6, 10 and 12 respectively.

6. A milkman has three different qualities of milk. 403 gallons of 1st quality, 465 gallons of 2nd quality and 496 gallons of 3rd quality. Find the least possible number of bottles of equal size in which different milk of different qualities can be filled without mixing

7. The LCM of two numbers is 4225 and the HCF is 13. If one number is 169. Then the other number is?

8. What should be the greatest number that divides 103, 106, 109 and 111 gives the remainder 3, 1, 4 and 1 respectively?

9. In a library, 15 books of botany, 20 books of zoology and 25 books of chemistry have to be arranged topic wise in stacks. If the books are all of the same thickness, then how many will be there in each stack?

10. In a public library, some books are ordered from a bookstore. After ordering 90 history books, 84 Environment science books and 120 Sociology books arrived. These books have to be stacked topic-wise in a rack. How many books will be there in each stack so that each stack will have the same height too?