Aptitude & Reasoning

LCM and HCF Aptitude Problems and Answers

Properties of HCF And LCM Problems

Multiple Choice Questions on LCM and HCF:

LCM and HCF

Question 1
Find HCF of 48, 168 and 324
A
12
B
18
C
36
D
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
A
96 m
B
0.96 m
C
9.6 m
D
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:
A
315
B
228
C
457
D
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.
A
420
B
540
C
425
D
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

A
184
B
364
C
74
D
94
Question 6
Find the H.C.F. of 108, 288 and 360.
A
32
B
24
C
36
D
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:
A
50
B
20
C
59
D
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.
A
154
B
137
C
150
D
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.
A
20
B
17
C
15
D
16
Question 10
Find the least number that being increased by 8 is divisible by 32, 36 and 40
A
1432
B
1400
C
1425
D
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?
A
4/35
B
35/37
C
12/41
D
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.
A
465
B
3234
C
3234
D
2884
Question 13
If the product of two numbers is 256 and their HCF is 4, then their LCM will be :
A
84
B
128
C
64
D
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.
A
845
B
827
C
999
D
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
A
Only one such pair exists
B
Many such paiirs exist
C
Only two such pairs exist
D
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 :
A
81
B
91
C
82
D
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?
A
172
B
164
C
174
D
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.
A
20
B
25
C
22
D
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
A
66
B
264
C
33
D
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:
A
23 ft
B
22 ft
C
28 ft
D
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.
A
61
B
45
C
47
D
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

A
324
B
320
C
230
D
640
Question 23
HCF of two numbers is 15 and their LCM is 180. If their sum is 105, then the numbers are:
A
35 and 70
B
50 and 75
C
30 and 70
D
45 and 60
Question 24
Find the H.C.F. of 2 x 32   x 5 x 74, 2 x 35 x 5 x 73,23 x 5 x 72
A
980
B
1020
C
840
D
720
Question 25
The largest number, which exactly divides the product of any three consecutive integers is
A
6
B
12
C
3
D
2
Question 26
Find the H.C.F. of 513, 1134 and 1215.
A
81
B
27
C
72
D
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
A
189
B
17
C
21
D
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
A
3603
B
7203
C
3600
D
7200
Question 29
The greatest number that will divide 187, 233 and 279 leaving the same remainder in each case is
A
36
B
30
C
56
D
46
Question 30
Find the least number which is divisible by all the numbers from 1 to 20 inclusive.

Related: Average (Reasoning Sample Paper)

A
255454515
B
151821276
C
20552124
D
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?
A
$ 31
B
$ 27
C
$ 29
D
$ 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.
A
12
B
9
C
5
D
2
Question 33
H.C.F of 96 and 108 is
A
3
B
6
C
12
D
4
Question 34
Find the greatest number that will divide 640, 710 and 1526 so as to leave 11, 7, 9 as remainders respectively.
A
29
B
36
C
42
D
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?
A
25
B
0
C
19
D
20
Question 36
Find the L.C.M. of 16, 24, 36 and 54.
A
256
B
516
C
432
D
378
Question 37
The largest natural number which exactly divides the product of any four consecutive natural num­bers is
A
12
B
120
C
6
D
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.
A
143
B
169
C
178
D
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?
A
2
B
1
C
4
D
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

A
25 cms
B
100 cms
C
50 cms
D
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.
A
2 and 6
B
9 and 14
C
2 and 4
D
6 and 4
Question 42
If LCM of two natural numbers is 36 and their sum is 30. Find the two numbers.
A
4, 26
B
15, 4
C
12, 18
D
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?
A
41 hours
B
20 hours
C
10 hours
D
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

A
90
B
100
C
99
D
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.
A
2884
B
3234
C
465
D
3834
Question 46
Find the L.C.M. of 72, 108 and 2100.
A
32270
B
37800
C
36700
D
24600
There are 46 questions to complete.
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Vishal Arora

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