# LCM and HCF Aptitude Problems and Answers

### Multiple Choice Questions on LCM and HCF:

Ques. Find HCF of 48, 168 and 324
(a) 12
(b) 18
(c) 28
(d) 36

Ans. (a)

Ques. Find the least number that being increased by 8 is divisible by 32, 36 and 40
(a) 1430
(b) 1400
(c) 1432
(d) 1425

Ans. (c)

Ques. 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

Ans. (c)

Ques. 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?
(a) 174
(b) 172
(c) 164
(d) 184

Ans. (d)

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Ques. 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:
(a) 25 cms
(b) 75 cms
(c) 50 cms
(d) 100 cms

Ans. (c)

Ques. 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

Ans. (b)

Ques. 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.
(a) 275
(b) 425
(c) 420
(d) 540

Ans. (c)

Ques. 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) 3834

Ans. (c)

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Ques. 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
(a) 0.96 m
(b) 9.6 m
(c) 96 m
(d) 960 m

Ans. (b)

Ques. Find the H.C.F. of 108, 288 and 360.
(a) 24
(b) 36
(c) 32
(d) 27

Ans. (b)

Ques. 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
(a) Only one such pair exists
(b) Only two such pairs exist
(c) Many such paiirs exist
(d) No such pair exists

Ans. (d)

Ques. 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?
(a) \$ 27
(b) \$ 28
(c) \$ 29
(d) \$ 31

Ans. (c)

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Ques. 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
(a) 9
(b) 21
(c) 17
(d) 189

Ans. (b)

Ques. 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.
(a) 147
(b) 150
(c) 137
(d) 154

Ans. (a)

Ques. 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
(a) 33
(b) 66
(c) 132
(d) 264

Ans. (c)

Ques. 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

Ans. (b)

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Ques. The greatest number that will divide 187, 233 and 279 leaving the same remainder in each case is
(a) 30
(b) 36
(c) 46
(d) 56

Ans. (c)

Ques. 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.
(a) 51
(b) 61
(c) 47
(d) 45

Ans. (a)

Ques. FindÂ the L.C.M. of 16, 24, 36 and 54.
(a) 516
(b) 256
(c) 432
(d) 378

Ans. (c)

Ques. The least multiple of 7 which leaves a remainder 4 when divided by 6, 9, 15 and 18 is
(a) 74
(b) 94
(c) 184
(d) 364

Ans. (d)

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Ques. Three men start together to travel the same way around a circular track of 11 kms in circumference. Their speeds are 4, 5 Â½ and 8 kms per hours respectively. When will they meet at the starting point?
(a) 10 hours
(b) 20 hours
(c) 22 hours
(d) 41 hours

Ans. (c)

Ques. The largest natural number which exactly divides the product of any four consecutive natural numÂ­bers is
(a) 6
(b) 12
(c) 24
(d) 120

Ans. (c)

Ques. Find the least multiple of 11 which when divided by 8, 12 and 16 leaves 3 as remainder.
(a) 100
(b) 90
(c) 99
(d) 88

Ans. (c)

Ques. The HCF of two numbers is 32 and their product is 10240. Find their L.C.M?
(a) 640
(b) 320
(c) 324
(d) 230

Ans. (b)

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Ques. 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

Ans. (d)

Ques. 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

Ans. (c)

Ques. Find the least multiple of 13 which when divided by 6, 8 and 12 leaves 5, 7 and 11 as remainder respectively.
(a) 211
(b) 178
(c) 169
(d) 143

Ans. (d)

Ques. 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.
(a) 720
(b) 999
(c) 827
(d) 845

Ans. (d)

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Ques. The largest number, which exactly divides the product of any three consecutive integers is
(a) 2
(b) 3
(c) 6
(d) 12

Ans. (c)

Ques. Find the H.C.F. of 513, 1134 and 1215.
(a) 72
(b) 99
(c) 27
(d) 81

Ans. (c)

Ques. 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

Ans. (c)

Ques. 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:
(a) 23 ft
(b) 28 ft
(c) 22 ft
(d) 52 ft

Ans. (c)

Ques. 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?
(a) 35/37
(b) 4/35
(c) 11/40
(d) 12/41

Ans. (b)

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Ques. Find the least number which is divisible by all the numbers from 1 to 20 inclusive.
(a) 232792560
(b) 255454515
(c) 151821276
(d) 20552124

Ans. (a)

Ques. Find the L.C.M. of 72, 108 and 2100.
(a) 24600
(b) 36700
(c) 32270
(d) 37800

Ans. (d)

Ques. 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.
(a) 17
(b) 15
(c) 16
(d) 20

Ans. (b)

Ques. 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
(a) 3600
(b) 3603
(c) 7200
(d) 7203

Ans. (d)

Ques. Find the H.C.F. of 23Â Â x 32Â Â Â x 5 x 74, 22Â Â x 35Â x 52Â Â x 73,23Â xÂ 53Â Â xÂ 72
(a) 980
(b) 1020
(c) 840
(d) 720

Ans. (a)

Ques. 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.
(a) 20
(b) 22
(c) 25
(d) 21

Ans. (d)

Ques. Four drums containing water have capacities 135 litres and 205 litres, 165 litres and 240 litres. Find the greatest capacity measure of the drums.
(a) 2
(b) 5
(c) 9
(d) 12

Ans. (b)

Ques. 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

Ans. (d)

Ques. If the Â LCM and HCF of two numbers is 324 and 3 respectively, If the one number is 12 then other number will be :
(a) 91
(b) 82
(c) 81
(d) 80

Ans. (d)

Ques. If the product of two numbers is 256 and their HCF is 4, then their LCM will be :
(a) 64
(b) 128
(c) 84
(d) None of these

Ans. (a)

Ques. If the LCM and HCF of two numbers is 54 and 4 respectively, then the product of two numbers will be:
(a) 315
(b) 216
(c) 457
(d) 228

Ans. (b)

Ques. The HCF and the LCM of a pair of numbers are 11 and 847 respectively. How many such distinct pairs are possible?
(a) 3
(b) 1
(c) 2
(d) 4

Ans. (c)

Ques. H.C.F of 96 and 108 is
(a) 4
(b) 6
(c) 12
(d) 3

Ans. (c)