### Multiple Choice Questions on LCM and HCF:

## LCM and HCF

Question 1 |

Find HCF of 48, 168 and 324

12 | |

18 | |

36 | |

28 |

Question 2 |

Three measuring rods are 64cm, 80cm and 96 cm in length. The least length of cloth (in meters) that can be measured exact number of times using any of the three rods is

96 m | |

0.96 m | |

9.6 m | |

960 m |

Question 3 |

If the LCM and HCF of two numbers is 54 and 4 respectively, then the product of two numbers will be:

315 | |

228 | |

457 | |

216 |

Question 4 |

The LCM of two numbers is 28 times their HCF. The sum of their LCM and HCF is 1740. If one of the numbers is 240, find the other number.

420 | |

540 | |

425 | |

275 |

Question 5 |

The least multiple of 7 which leaves a remainder 4 when divided by 6, 9, 15 and 18 is

**Related:** Letter Sequence Sample paper

184 | |

364 | |

74 | |

94 |

Question 6 |

Find the H.C.F. of 108, 288 and 360.

32 | |

24 | |

36 | |

27 |

Question 7 |

The least number which when divided by 4, 6, 8, 12 and 16 leaves a remainder of 2 in each case is:

50 | |

20 | |

59 | |

43 |

Question 8 |

A gardener had a number of shrubs to plant in rows. At first he tried to plant 8, then 12 and then 16 in a row but he had always 3 shrubs left with him. On trying 7 he had none left. Find the total number of shrubs.

154 | |

137 | |

150 | |

147 |

Question 9 |

Six bells commencing tolling together and toll at intervals of 2,4,6,8,10 and 12 seconds respectively. In 30 minutes, how many times do they toll together.

20 | |

17 | |

15 | |

16 |

Question 10 |

Find the least number that being increased by 8 is divisible by 32, 36 and 40

1432 | |

1400 | |

1425 | |

1430 |

Question 11 |

The sum of two numbers is 36 and their HCF and LCM are 3 and 105 respectively. The sum of the reciprocals of the said two numbers is?

4/35 | |

35/37 | |

12/41 | |

11/40 |

Question 12 |

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.

465 | |

3234 | |

3234 | |

2884 |

Question 13 |

If the product of two numbers is 256 and their HCF is 4, then their LCM will be :

84 | |

128 | |

64 | |

None of these |

Question 14 |

A gardener was asked to plant flowers In a row containing equal number of plants. He tried to plant 6, 8, 10 and 12 In each row, but 5 plants left in each case but when he planted 13 in arrow, no plant was left. Find the least no. of plants with him.

845 | |

827 | |

999 | |

720 |

Question 15 |

About the number of pairs which have 16 as their H.C.F. and 136 as their L.C.M., we can definitely say that

Only one such pair exists | |

Many such paiirs exist | |

Only two such pairs exist | |

No such pair exists |

Question 16 |

If the LCM and HCF of two numbers is 324 and 3 respectively, If the one number is 12 then other number will be :

81 | |

91 | |

82 | |

80 |

Question 17 |

What is the least number of cut pieces of equal length that can be cut out of two lengths 10 metres 857 mllliimetres and 15 metres 87 millimetres?

172 | |

164 | |

174 | |

184 |

Question 18 |

In a seminar the number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required, where in each room the same number of participants are to be seated; and all of them being in the same subject.

20 | |

25 | |

22 | |

21 |

Question 19 |

The H.C.F. and L.C.M. of two numbers are 44 and 264 respectively. If the first number is divided by 2. the quotient is 44. The other number is

66 | |

264 | |

33 | |

132 |

Question 20 |

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 feet lengths. For minimum waste the lengths to be ordered should be:

23 ft | |

22 ft | |

28 ft | |

52 ft |

Question 21 |

A merchant has three kinds of milk : 435 litres, 493 litres and 551 litres. Find the least number of casks of equal size required to store all the milk without mixing.

61 | |

45 | |

47 | |

51 |

Question 22 |

The HCF of two numbers is 32 and their product is 10240. Find their L.C.M?

**Related:** Number Series Practice Problems

324 | |

320 | |

230 | |

640 |

Question 23 |

HCF of two numbers is 15 and their LCM is 180. If their sum is 105, then the numbers are:

35 and 70 | |

50 and 75 | |

30 and 70 | |

45 and 60 |

Question 24 |

Find the H.C.F. of 2

^{3 }^{ }x 3^{2 }^{ }x 5 x 7^{4}, 2^{2 }^{ }x 3^{5}x 5^{2 }^{ }x 7^{3},2^{3}^{ }x^{ }5^{3 }^{ }x^{ }7^{2}980 | |

1020 | |

840 | |

720 |

Question 25 |

The largest number, which exactly divides the product of any three consecutive integers is

6 | |

12 | |

3 | |

2 |

Question 26 |

Find the H.C.F. of 513, 1134 and 1215.

81 | |

27 | |

72 | |

99 |

Question 27 |

The L.C.M. of two numbers is 63 and their H.C.F. is 9. If one of the numbers is 27, the other number will be

189 | |

17 | |

21 | |

9 |

Question 28 |

A heap of stones can be made in groups of 21 but when made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case, The number of stones in the heap is

3603 | |

7203 | |

3600 | |

7200 |

Question 29 |

The greatest number that will divide 187, 233 and 279 leaving the same remainder in each case is

36 | |

30 | |

56 | |

46 |

Question 30 |

Find the least number which is divisible by all the numbers from 1 to 20 inclusive.

**Related:** Average (Reasoning Sample Paper)

255454515 | |

151821276 | |

20552124 | |

232792560 |

Question 31 |

A worker was engaged for a certain number of days and was promised to be paid $ 1189. He remained absent for some days and was paid $ 1073 only. What were his daily wages?

$ 31 | |

$ 27 | |

$ 29 | |

$ 28 |

Question 32 |

Four drums containing water have capacities 135 litres and 205 litres, 165 litres and 240 litres. Find the greatest capacity measure of the drums.

12 | |

9 | |

5 | |

2 |

Question 33 |

H.C.F of 96 and 108 is

3 | |

6 | |

12 | |

4 |

Question 34 |

Find the greatest number that will divide 640, 710 and 1526 so as to leave 11, 7, 9 as remainders respectively.

29 | |

36 | |

42 | |

37 |

Question 35 |

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?

25 | |

0 | |

19 | |

20 |

Question 36 |

Find the L.C.M. of 16, 24, 36 and 54.

256 | |

516 | |

432 | |

378 |

Question 37 |

The largest natural number which exactly divides the product of any four consecutive natural numbers is

12 | |

120 | |

6 | |

24 |

Question 38 |

Find the least multiple of 13 which when divided by 6, 8 and 12 leaves 5, 7 and 11 as remainder respectively.

143 | |

169 | |

178 | |

211 |

Question 39 |

The HCF and the LCM of a pair of numbers are 11 and 847 respectively. How many such distinct pairs are possible?

2 | |

1 | |

4 | |

3 |

Question 40 |

The floor of a room of dimensions 6.5m x 4.0 m is to be paved with square marble slabs. The length of the largest possible slab is:

**Related:** Data Interpretation Sample Paper

25 cms | |

100 cms | |

50 cms | |

75 cms |

Question 41 |

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

2 and 6 | |

9 and 14 | |

2 and 4 | |

6 and 4 |

Question 42 |

If LCM of two natural numbers is 36 and their sum is 30. Find the two numbers.

4, 26 | |

15, 4 | |

12, 18 | |

9, 21 |

Question 43 |

Three men start together to travel the same way around a circular track of 11 kms in circumference. Their speeds are 4, 5 ½ and 8 kms per hours respectively. When will they meet at the starting point?

41 hours | |

20 hours | |

10 hours | |

22 hours |

Question 44 |

Find the least multiple of 11 which when divided by 8, 12 and 16 leaves 3 as remainder.

**Related:** Direction Test Sample Paper

90 | |

100 | |

99 | |

88 |

Question 45 |

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.

2884 | |

3234 | |

465 | |

3834 |

Question 46 |

Find the L.C.M. of 72, 108 and 2100.

32270 | |

37800 | |

36700 | |

24600 |

There are 46 questions to complete.

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