Maths: Important Topic: 
Self Assessment Test

Problems on H.C.F and L.C.M
QNo.1    Find the least square number which is divisible by 10, 12, 15 and 18? 0
1600
900
3600
2500
QNo.2    Three men start together to travel the same way around a circular track of 11 kilometers in circumference. Their speeds are 4, 5 and 8 kilometers per hour respectively. When will they meet at a starting point? 2
11 hours
12 hours
220 hours
22 hours
QNo.3    Find the least multiple of 13 which when divided by 6, 8 and 12 leaves 5, 7 and 11 as remainders respectively?
143
169
260
221
QNo.4    Find the least number which when divided by 6, 7, 8, 9 and 10 leaves 1, 2, 3, 4 and 5 as remainders respectively, but when divided by 19 leaves no remainder? 0
5073
5016
5054
5035
QNo.5    Find the least number which when divide by 2, 3, 4, 5 and 6 leaves 1, 2, 3, 4 and 5 as remainders respectively, but when divided by 7 leaves no remainder? 0
210
119
126
154
QNo.6    A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap? 0
7203
2403
3603
4803
QNo.7    Find the greatest number of four digits which when divided by 10, 15, 21 and 28 leaves 4, 9, 15 and 22 as remainders respectively? 0
9654
9666
9664
9864
QNo.8    Find the least number which when divided by 35 leaves remainder 25, when divided by 25 leaves remainder 15 and when divided by 15 leaves remainder 5? 0
420
515
435
518
QNo.9    What is the least number which when divided by 8, 12, 18 and 24 leaves the remainders 4, 8, 14 and 20 respectively? 0
78
68
58
None
QNo.10    Two numbers 4242 and 2903 when divided by a certain number of three digits, leave the same remainder. Find the number? 0
101
103
107
113
QNo.11    There are four prime numbers written in ascending order of magnitude. The product of the first three is 385 and of the last three is 1001. Find the fourth number? 0
5
7
11
13
QNo.12    There are four prime numbers written in ascending order of magnitude. The product of the first three is 7429 and of the last three is 12673. Find the fourth number? 0
17
29
23
31
QNo.13    How many minimum number’s of whole square slabs are required for paving the floor 12.96 meters long and 3.84 meters side? 0
216
192
108
256
QNo.14    A room is 4 meters 37 cm long and 3 meters 23cm broad. It is required to pave the floor with minimum square slabs. Find the number of slabs required for this purpose? 0
485
431
391
381
QNo.15    Find the size of the largest square slabs which can be paved on the floor of a room 5 meters 44 cm long and 3 meters 74 cm broad? 0
56
42
38
34
QNo.16    A wholesale tea dealer 408 kilograms, 468 kilograms and 516 kilograms of three different qualities of tea. He wants it all to be packed into boxes of equal size without mixing. Find the capacity of the largest possible box? 0
50
36
24
12
QNo.17    A merchant has three different types of milk: 435 liters, 493 liters and 551 liters. Find the least number of casks of equal size required to store all the milk without mixing. 0
51
61
47
45
QNo.18    Find the greatest number which is such that when 697, 909 and 1227 are divided by it, the remainders are all the same? 0
53
112
108
106
QNo.19    Find the greatest number which will divide 25, 73 and 97 as so to leave the same remainder in each case? 0
12
18
24
32
QNo.20    An officer was appointed on maximum daily wages on contract money of Rs. 4956. But on being absent for some days, he was paid only Rs. 3894. For how many days was he absent? 0
3
4
5
6
QNo.21    A man was employed on the promise that he will be paid the highest wages per day. The contract money to be paid was Rs. 1189. Finally he was paid only Rs. 1073. For how many days did he actually work? 0
39
40
37
35
QNo.22    In finding the HCF of two numbers, the last divisor was 41 and the successive quotients, starting from the first, where 2, 4 and 2. The numbers are______? 0
700,400
820,360
800,500
820,369
QNo.23    Least perfect square number, exactly divisible by 21, 36 and 56 is_________? 0
3600
504
441
7056
QNo.24    HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is_______? 0
36
66
132
264
QNo.25    Five bells first begin to toll together and then at intervals of 5, 10, 15, 20 and 25 seconds respectively. After what interval of time will they toll again together? 0
5 min
5.5 min
5.2 min
None
QNo.26    Find the least number of five digits which is exactly divisible by 12, 15 and 18? 0
1080
10080
10025
11080
QNo.27    The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is________? 0
1994
1494
1349
1496
QNo.28    A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is_______? 0
31
41
51
61
QNo.29    The smallest number when increased by ” 1 ” is exactly divisible by 12, 18, 24, 32 and 40 is__________? 0
1439
1440
1459
1449
QNo.30    The least number of five digits that have 144 their HCF is__________? 0
10085
10080
10075
10070
QNo.31    The greatest number of four digits that have 144 for their HCF is___________? 0
9930
9903
9935
9936
QNo.32    The least number of four digits which is divisible by 4, 6, 8 and 10 is_________? 0
1080
1085
1075
1095
QNo.33    The greatest number of five digits which is divisible by 32, 36, 40, 42 and 48 is_________? 0
90730
90725
90715
90720
QNo.34    The product of two digits number is 2160 and their HCF is 12. The numbers are________? 0
(36,60)
(12,180)
(96,25)
(72,30)
QNo.35    Four bells begin to toll together respectively at the intervals of 8, 10, 12 and 16 seconds. After how many seconds will they toll together again? 0
246 seconds
242 seconds
240 seconds
243 seconds
QNo.36    The least number which when diminished by 7 is divisible by 21, 28, 36 and 45 is________? 0
1267
1265
1261
68
QNo.37    The least number which when add 3 to it, completely divided 8, 12 and 18 is_______? 0
71
70
69
68
QNo.38    The least number which when divided by 8, 12 and 16, leave in each remainder 3, is_______? 0
71
70
69
51
QNo.39    The least square number which divides 8, 12 and 18 is______?
100
121
64
144
QNo.40    The least number which when divided by 16, 18 and 21, leave the remainder 3, 5 and 8 respectively is___________? 0
982
893
1024
995
QNo.41    The product of two numbers is 2025 and their HCF is 15 their LCM is____________? 0
2040
2010
135
150
QNo.42    Find the H.C.F of 204, 1190 and 1445? 0
34
17
.85
204
QNo.43    Find the H.C.F of 12, 16, 18 and 24? 0
1
2
.F of 12, 16, 18 and 24?0 A. 1B. 2 3
4
QNo.44    HCF of 3/16, 5/12, 7/8 is__________? 0
2/47
3/47
1/48
5/48
QNo.45    LCM of 1/3, 5/6, 5/4, 10/7 is_________? 0
10/7
10
10/11
11/10
QNo.46    LCM of 87 and 145 is_______? 0
1305
435
875
48
QNo.47    LCM of 18 and 27 is_________? 0
85
89
54
91
QNo.48    Greatest Common Divisor of two numbers is 8 while their Least Common Multiple is 144. Find the other number if one number is 16. 0
108
96
72
36
QNo.49    The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is_________? 0
28
32
40
64
QNo.50    Which of the following has the most number of divisors? 0
99
101
176
182
QNo.51    The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is: 0
3
13
23
33
QNo.52    The least number of four digits which is divisible by 15, 25, 40 and 75 is_________? 0
9000
9400
9600
9800
QNo.53    The smallest fraction, which each of 6/7, 5/14, 10/21 will divide exactly is_________? 0
30/7
30/98
60/147
50/294
QNo.54    What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30? 0
196
630
1260
2520
QNo.55    Which of the following fractions is the largest? 0
7/8
13/16
31/40
63/80
QNo.56    The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is___________? 0
276
299
322
345
QNo.57    The H.C.F of two numbers is 8. Which of the following can never be their L.C.M? 0
24
48
56
60
QNo.58    The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 10, then their difference is__________? 0
10
46
70
90
QNo.59    The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275, then the other is__________? 0
279
283
308
318
QNo.60    The H.C.F and L.C.M of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1:4, then the larger of the two numbers is____________? 0
12
48
84
108
QNo.61    Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is: 0
40
80
120
200
QNo.62    The L.C.M of two numbers is 48. The numbers are in the ratio 2:3. The sum of numbers is__________? 0
28
32
40
64
QNo.63    Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is________? 0
75
81
85
89
QNo.64    The product of two numbers is 2028 and their H.C.F is 13. The number of such pairs is__________? 0
1
2
3
4
QNo.65    The product of two numbers is 4107. If the H.C.F of these numbers is 37, then the greater number is_________? 0
101
107
111
185
QNo.66    The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is__________? 0
4
6
8
12
QNo.67    The ratio of numbers is 3:4 and their H.C.F is 4. Their L.C.M is__________? 0
12
16
24
48
QNo.68    Find the lowest common multiple of 24, 36 and 40. 0
120
240
360
480
QNo.69    Find the highest common factor of 36 and 84. 0
4
6
12
18
QNo.70    Which of the following has most number of divisors? 0
99
101
176
182
QNo.71    A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the room? 0
110
124
96
117
QNo.72    Find the greatest number that, while dividing 47, 215 and 365, gives the same remainder in each case? 0
3
4
5
6
QNo.73    Find the greatest number which, while dividing 19, 83 and 67, gives a remainder of 3 in each case? 0
16
17
18
19
QNo.74    Find the greatest number that exactly divides 35, 91 and 840? 0
5
6
7
8
QNo.75    Find the lowest 4-digit number which when divided by 3, 4 or 5 leaves a remainder of 2 in each case? 0
1020
1026
1030
1022
QNo.76    Find the greatest 4-digit number exactly divisible by 3, 4 and 5? 0
9985
9960
9957
9975
QNo.77    Find the smallest number which when increased by 5, divisible by 6, 9, 15, 20 and 24? 0
344
355
366
377