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Aptitude - HCF and LCM

MCQ

Q 1.

Jai, Veeru and Dhanno are friends and they have 3 numbers 2a, 4a and 8a respectively. Find the LCM of their numbers.

Option: A

2a

Option: B

4a

Option: C

8a

Option: D

16a

C

LCM = 2x2x2xa = 8a

Q 2.

Find the LCM of 1/3, 2/9, 5/6 and 4/27.

Option: A

10/3

Option: B

20/3

Option: C

3/10

Option: D

3/20

B

Required LCM = LCM of numerators / HCF of denominators

= LCM(1,2,5,4) / HCF(3,9,6,27)

= 20/3

Q 3.

Find the HCF of 1/2 and 3/4.

Option: A

1/3

Option: B

1/4

Option: C

4/3

Option: D

2/3

B

Required HCF = HCF of numerators / LCM of denominators

= HCF(1,3) / LCM(2,4)

= 1/4

Q 4.

The product of two coprime numbers is 117. Find their LCM.

Option: A

117

Option: B

111

Option: C

171

Option: D

None of these

A

HCF of two coprime numbers = 1.

We know, that Product of two numbers = HCF of the numbers x LCM of the numbers.

Therefore, 117 = 1 x LCM

or, LCM = 117

Or, we can say that LCM of two coprime numbers is equal to the product of the numbers.

Q 5.

If the HCF of two numbers is 8 then which of the following can never be their LCM.

Option: A

60

Option: B

48

Option: C

56

Option: D

24

A

LCM of two numbers is always a multiple of their HCF.

Given, HCF = 8

Now, from the list of options we see that 60 is not a multiple of 8.

Hence, 60 can never be the LCM of the two numbers.

Q 6.

Rocky has two numbers in the ratio 3:4. Find the LCM if their HCF is 4.

Option: A

12

Option: B

24

Option: C

36

Option: D

48

D

Let the two numbers be 3q and 4q where q is the HCF.

Given, HCF = 4.

So, the two numbers are 12 and 16.

Therefore, the required LCM = 48

Q 7.

Jai and Veeru are running in opposite direction on a circular path at Eden Garden, Calcutta. Jai takes 5 minutes while Veeru takes 6 minutes to complete a lap. If they decided to run 6 laps then find the number of time they will cross each other.

Option: A

1

Option: B

2

Option: C

3

Option: D

4

A

Total time taken by Jai to complete a lap = 5 minutes

Total time taken by Veeru to complete a lap = 6 minutes

Total time taken by Jai to complete 6 laps = 5x6 = 30 minutes.

Total time taken by Veeru to complete 6 laps = 6x6 = 36 minutes.

HCF of 5 minutes and 6 minutes is 30 minutes.

So, they will cross only once.

Q 8.

Find the greatest 3 digit number which when divided by 6, 9 and 12 leaves 3 as remainder in each case.

Option: A

965

Option: B

975

Option: C

985

Option: D

995

B

The greatest 3 digit number is 999.

LCM of 6, 9 and 12 is 36.

When we divide 999 by 36 we get 27 as remainder.

So, the required 3 digit number is (999 - 27 + 3) i.e., 975.

Q 9.

Find the least number which when divided by 12, 16 and 18 leaves 5 as remainder in each case.

Option: A

148

Option: B

149

Option: C

150

Option: D

151

B

LCM of 12, 16 and 18 = 144

The required least number = 144+5 = 149

Q 10.

Find the HCF of (x4 - y4) and (x6 - y6).

Option: A

x4 - y4

Option: B

x3 - y3

Option: C

x2 - y2

Option: D

x - y

C

f(x) = (x4 - y4)

= (x2)2 - (y2)2

= (x2 - y2)(x2 + y2)

= (x - y)(x + y)(x2 + y2)

 

g(x) = (x6 - y6)

= (x3)2 - (y3)2

= (x3 - y3)(x3 + y3)

= (x - y)(x2 - y2 + xy) (x + y)(x2 + y2 - xy)

= (x - y)(x + y) (x2 - y2 + xy)(x2 + y2 - xy)

 

Common factor in f(x) and g(x) = (x - y)(x + y) = (x2 - y2)

Therefore, HCF = (x2 - y2)

Q 11.

Express 252 as a product of primes

Option: A

2x3x3x3x7

Option: B

2x2x2x3x7

Option: C

3x3x3x3x7

Option: D

2x2x3x3x7

D
Q 12.

Express 1095/1168 in simplest form

Option: A

17/26

Option: B

25/26

Option: C

15/16

Option: D

13/16

C
Q 13.

Find the HCF of 3x5x7x11, 2x2x2x2x3x3x5x5x5x7 and 2x2x2x3x3x3x5x5x7x7

Option: A

105

Option: B

27720

Option: C

2310

Option: D

1155

A
Q 14.

Find the HCF of

4x27x3125, 5x11x16x49x81 and 7x8x9x25

Option: A

1260

Option: B

540

Option: C

180

Option: D

360

C
Q 15.

Find the LCM of 24, 36 and 40

Option: A

120

Option: B

240

Option: C

360

Option: D

480

C
Q 16.

Find the LCM of 22, 54, 108, 135 and 198

Option: A

330

Option: B

1980

Option: C

5940

Option: D

11880

C
Q 17.

Find GCD of 0.36, 0.9 and 1.08

Option: A

0.18

Option: B

0.90

Option: C

0.108

Option: D

0.27

A
Q 18.

Find the value of X if HCF of X, 3240 and 3600 is 36 and their LCM is 24x35x52x72

Option: A

22x35x72

Option: B

25x52x72

Option: C

23x35x72

Option: D

22x53x72

A
Q 19.

Find the three numbers if they are in the ratio 1:2:3 and their HCF is 12

Option: A

10, 20, 30

Option: B

12, 24, 36

Option: C

4, 8, 12

Option: D

5, 10, 15

B
Q 20.

Find the LCM if two numbers are in the ratio 3:4 and their HCF is 4

Option: A

12

Option: B

48

Option: C

16

Option: D

24

B
Q 21.

If AxB = 4107 and HCF of A and B is 37, then find the geater number

Option: A

111

Option: B

185

Option: C

107

Option: D

101

A
Q 22.

Three numbers are coprime to each other and the product of the first two is 551 and the product of the last two is 1073 then find the sum of the three numbers.

Option: A

81

Option: B

85

Option: C

75

Option: D

89

B
Q 23.

Find the sum of two numbers if they are in the ratio 2:3 and their LCM is 48

Option: A

28

Option: B

64

Option: C

40

Option: D

32

C
Q 24.

Find the HCF of three numbers if they are in the ratio 3:4:5 and their LCM is 2400

Option: A

200

Option: B

40

Option: C

80

Option: D

120

B
Q 25.

Find the value of X if LCM of X and 275 is 7700 and HCF of X and 275 is 11.

Option: A

318

Option: B

308

Option: C

283

Option: D

279

B
Q 26.

Two numbers are in the ratio 1:4 and their HCF and LCM are 84 and 21 respectively. Find the greater number.

Option: A

108

Option: B

84

Option: C

48

Option: D

12

B
Q 27.

Find the difference if the sum of two numbers is 10 and their HCF and LCM are 5 and 495 respectively.

Option: A

10

Option: B

46

Option: C

70

Option: D

90

A
Q 28.

Find the LCM if product of two co-prime numbers is 117

Option: A

Cannot be found

Option: B

Equal to their HCF

Option: C

1

Option: D

117

D
Q 29.

If x and y are two prime numbers such that x>y and LCM of x and y is 161. Then find the value of 3y-x

Option: A

1

Option: B

2

Option: C

-1

Option: D

-2

D
Q 30.

Which of the following can never be the LCM of two numbers if their HCF is equal to 8

Option: A

48

Option: B

60

Option: C

24

Option: D

56

B
Q 31.

The greatest possible length which can be used to exactly measure the lengths 12m 95cm, 7m and 3m 85cm is

Option: A

45cm

Option: B

35cm

Option: C

25cm

Option: D

15cm

B
Q 32.

There are 1001 pens and 910 pencils and you have to find the maximum number of students to distribute these pens and pencils in such a way that each student gets same number of pens and same number of pencils.

Option: A

1001

Option: B

910

Option: C

1911

Option: D

91

D
Q 33.

A rectangular steel sheet 3.78m long and 5.25m wide is to be cut into square pieces, each of same size. Find the largest size of the piece which could be cut.

Option: A

21cm

Option: B

42cm

Option: C

14cm

Option: D

None of these

A
Q 34.

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

Option: A

4

Option: B

9

Option: C

7

Option: D

13

A
Q 35.

Find the greatest number which on dividing 1657 and 2037 leaves remainder 6 and 5 respectively.

Option: A

305

Option: B

123

Option: C

235

Option: D

127

D
Q 36.

Find the greatest number of 4 digits which is divisible by 15, 25, 40 and 75

Option: A

9000

Option: B

9400

Option: C

9600

Option: D

9800

C
Q 37.

Find the least number which should be added to 2497 so that the sum is exactly divisible by 3,4,5 and 6.

Option: A

3

Option: B

13

Option: C

23

Option: D

33

C
Q 38.

Find the least number which when divided by 12, 15, 20 and 54 leaves 8 as remainder in each case.

Option: A

504

Option: B

536

Option: C

544

Option: D

548

D