Problems On HCF And LCM

Q1) Greatest Common Divisor of two numbers is 8 while their Least Common Multiple is 144. Find the other number if one number is 16.

a. 108
b. 96
c. 72
d. 36
ANSWER: 72

2) LCM of two numbers is 138. But their GCD is 23. The numbers are in a ratio 1:6. Which is the largest number amongst the two?

a. 46
b. 138
c. 69
d. 23
ANSWER: 138

3) The least common multiple of two numbers is 168 and highest common factor of them is 12. If the difference between the numbers is 60, what is the sum of the numbers?

a. 108
b. 96
c. 122
d. 144
ANSWER: 108

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4) If least common multiple of two numbers is 225 and the highest common factor is 5 then find the numbers when one of the numbers is 25?

a. 75
b. 65
c. 15
d. 45
ANSWER: 45

5) The greatest number of four digits which is divisible by 15, 25, 40, 75 is

a. 600
b. 9000
c. 9600
d. 9400
ANSWER: 9600

6) What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case a remainder 2 but which when divided by 13 leaves no remainder?

a. 312
b. 962
c. 1586
d. 1562
ANSWER: 1586

7) When a number is divided by 893 the remainder is 193. What will be the remainder when it is divided by 47?

a. 19
b. 5
c. 33
d. 23
ANSWER: 5

8) The sum of two numbers is 156 and their HCF is 13. The numbers of such number pairs is

a. 2
b. 5
c. 4
d. 3
ANSWER: 2

9) The L.C.M. of two numbers is 14560 and their H.C.F. is 13. If one of them is 416, the other is

a. 460
b. 455
c. 450
d. 445
ANSWER: 455

10) The greatest length of the scale that can measure exactly 30 cm, 90 cm, 1 m 20 cm and 1 m 35 cm lengths is

a. 5 cm
b. 10 cm
c. 15cm
d. 30 cm
ANSWER: 15cm

11) What will be least number of marbles with Rohit if he can arrange them in rows of 18, 10 and 15 marbles each as well as make a perfect solid square out of all the marbles?

a. 133
b. 43
c. 90
d. 900
ANSWER: 900

12) 3 birds fly along the circumference of a jungle. They complete one round in 27 minutes, 45 minutes and 63 minutes respectively. Since they start together, when will they meet again at the starting position?

a. 945 minutes
b. 126 minutes
c. 135 minutes
d. 9 hours
ANSWER: 945 minutes

13) What least possible 4-digit number, when divided by 12, 16, 18 and 20 leaves 21 as remainder?

a. 36
b. 133
c. 144
d. 1461
ANSWER: 1461

14) 5 clocks ring automatically at intervals of 12 minutes, 8 minutes, 3 minutes, 4 minutes and 10 minutes, respectively. In 8 hours from the moment they start, how many times will they ring together?

a. 12 times
b. 5 times
c. 3 times
d. 4 times
ANSWER: 4 times

15) What least number when divided by 36, 24 and 16 leaves 11 as remainder in each case?

a. 36
b. 133
c. 144
d. 155
ANSWER: 155

16) If (x – 4) is the HCF of x2 – 8x + 15 and x2 – kx +1 , then what is k?

a. 8/15
b. 4
c. 5
d. 15/8
ANSWER: 4

17) What least number when divided by 20, 48 and 36 leaves the remainders 13, 41 and 29, respectively

a. 720
b. 713
c. 727
d. 187
ANSWER: 71

18) There are 3 equilateral triangles with sides 114cm, 76cm and 152 cm. What maximum size scale can measure them exactly

a. 19 cm
b. 21 cm
c. 38 cm
d. None of the above
ANSWER: 38 cm

19) What greatest number divides 17, 42 and 93 and leaves remainders 4, 3 and 15, respectively?

a. 89
b. 78
c. 13
d. 17

ANSWER: 13

20) What largest number will divide 47, 35 and 27 leaving same remainder in each case? What will be the common remainder?

a. 9, 1
b. 1, 9
c. 4, 3
d. 3, 4
ANSWER: 4, 3

21) What is HCF of 36/75, 48/150 , 72/135?

a. 12/1350
b. 150/36
c. 1350/36
d. 72/225
ANSWER: 12/1350

22) Rajesh had to arrange his books in uniform groups. He makes groups of 4 books each. But 3 books are left. He tries it with groups of 5 books each. But still 3 books are left. 3 books are still left when he tried with groups of 9 or 10 books each. How many books does he have?

a. 90
b. 180
c. 900
d. 183
ANSWER: 183

23) HCF and LCM of two numbers is 8 and 96. Sum of those numbers is 56. Then what is sum of their reciprocals?

a. 1/56
b. 7/96
c. 1/96
d. 1/8

ANSWER: 7/96

24) What is LCM of 36/225, 48/150 , 72/65 ?

a. 36/65
b. 144/5
c. 72/225
d. 288/5
ANSWER: 144/5

25) Manoj wants to paste wallpaper on wall of his room. The wall is 4 meters and 50 cm in length and 3 meters and 50 cm in height. But the wall should be covered completely only by square pieces of wallpaper having same size. What is the number of maximum sized wallpaper squares needed to cover the walls completely?

a. 8
b. 15.75
c. 63
d. 12
ANSWER: 63

26) The ratio of two numbers is 5 : 6 and their LCM is 480, then their HCF is?

a. 16
b. 96
c. 12
d. 240
ANSWER: 16

27) The length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively. Find how many minimum number of square tiles would be required to cover it completely?

a. 375
b. 2570
c. 2800
d. 3315
e. None of these
ANSWER: 3315

28) The L.C.M. of two number is 60. The numbers are in the ratio 4 : 5. Find the sum of numbers.

a. 27
b. 33
c. 38
d. 45
ANSWER: 27

29) The L.C.M. Of 2, 2.7 and 0.09 is:

a. 5.4
b. 0.54
c. 0.054
d. 54

ANSWER: 54

30) The length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively. Find how many minimum number of square tiles would be required to cover it completely?

a. 375
b. 2570
c. 2800
d. 3315
e. None of these

ANSWER: 3315

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