(IGP) IAS Pre Paper - 2: GS - Basic Numeracy - HCF & LCM (MCQ -3)

1. How many numbers less than 10,000 are there which are divisible by 21, 35 and 63?
(a) 33
(b) 32
(c) 38
(d) 31

2. Find the side of the largest possible square slabs which can be paved on the floor of a room 2m 50 cm long and 1 m 50 cm broad. Also find the  number of such slabs to pave the floor.
(a) 40, 18
(b) 30, 15
(c) 50, 15
(d) 20, 25

3. What is the largest number which when divides 1475, 3155 and 5255 leaves the same remainder in each case?
(a) 220
(b) 420
(c) 350
(d) 540

4. A florist has 200 roses and 180 jasmines with him. He was asked to make garlands of flowers with only roses or only jasmines each containing the same number of flowers. What will be the largest number of flowers, he can join together without leaving a single flower?
(a) 16
(b) 17
(c) 20
(d) 19

5. The HCF and LCM of a pair of numbers are 12 and 926 respectively. How many such distinct pairs are possible?
(a) 3
(b) 7
(c) 1
(d) 0

6. Find the LCM of 5/2, 8/9, 11/14.
(a) 290
(b) 380
(c) 420
(d) 440

7. Which of the following numbers gives the same remainder when it divides 2272 and 875?
(a) 173
(b) 127
(c) 129
(d) 139

8. The HCF and LCM of two numbers are 18 and 3780 respectively. If one of them is 540, then the second one is:
(a) 146
(b) 126
(c) 118
(d) 117

9. The LCM of two numbers is 864 and their HCF is 144. If one of the numbers is 288, the other number is:
(a) 577
(b) 444
(c) 432
(d) 148

10. The least number which when divided by 4, 6, 8, 12 and 16 leaves a remainder of 2 in each case is:
(a) 20
(b) 43
(c) 50
(d) 59

11. The HCF of two numbers is 8. Which one of the following can never be their LCM?
(a) 32
(b) 24
(c) 48
(d) 60

12. The product of the LCM and HCF of two numbers is 24. The difference of the two numbers is 2. Find the numbers.
(a) 2 and 6
(b) 9 and 14
(c) 2 and 4
(d) 6 and 4

13. Find the greatest number that will divide 640, 710 and 1526 so as to leave 11, 7, 9 as remainders respectively.
(a) 36
(b) 37
(c) 42
(d) 29

14. If LCM of two natural numbers is 36 and their sum is 30. Find the two numbers.
(a) 15, 4
(b) 12, 18
(c) 9, 21
(d) 4, 26

15. Two persons A and B walk round a circle whose diameter is 1.4 km. A walks at a speed of 165 meters per minute while B walks at a speed of 110 meters per minute. If they both start at the same time, from the same point and walk in the same direction, at what interval of time would they both be at the same starting point again?
(a) 3h
(b) 4/3h
(c) 5/3h
(d) 7/2h

16. There are 5 consecutive natural numbers with LCM as 60. The product of the first two numbers is equal to the 5th number. What is the sum of the 5 numbers?
(a) 0
(b) 19
(c) 20
(d) 25

17. Find the least number which when divided by 16, 18 and 20 leaves a remainder 4 in each case, but is completely divisible by 7.
(a) 465
(b) 3234
(c) 2884
(d) 3234

18. HCF of two numbers is 15 and their LCM is 180. If their sum is 105, then the numbers are:
(a) 30 and 70
(b) 35 and 70
(c) 50 and 75
(d) 45 and 60

19. A certain type of board is sold in lengths of multiples of 2 feet. The shortest board sold is 6 feet, and the longest is 24 feet. A builder needs a large quantity of this type of board in 5 1 2 feet lengths. For minimum waste the lengths to be ordered should be:
(a) 23 ft
(b) 28 ft
(c) 22 ft
(d) 52 ft

20. The LCM and HCF of two positive numbers is 1000 and 50 respectively. Which of the following could be the pair of such numbers?
(a) 150 and 200
(b) 175 and 300
(c) 50 and 100
(d) 200 and 250

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