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Arithmetic Ability
Problems On H.C.F And L.C.M
Quiz 4
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Q.1
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:
276
299
322
345
Q.2
The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
74
94
184
364
Q.3
The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is = ?
1677
1683
2523
3363
Q.4
A gardener has to plant trees in rows containing equal number of trees. If he plants in rows of 6, 8, 10 or 12 then five trees are left unplanted. But if he plants in rows of 13 trees each, then no tree is left. What is the number of trees that the gardener plants ?
485
725
845
None of these
Q.5
Which greatest number will divide 3026 and 5053 leaving remainders 11 and 13 respectively ?
15
30
45
60
Q.6
Find the greatest number that will divide 964, 1238 and 1400 leaving remainders 41, 31, and 51 respectively = ?
61
71
73
81
Q.7
The HCF of x
^{6}
- 1 and x
^{4}
+ 2x
^{3}
- 2x
^{1}
- 1 is = ?
x
^{2}
+ 1
x - 1
x
^{2}
- 1
x + 1
Q.8
Find the least number which when divided by 12, leaves a remainder of 7; when divided by 15, leaves a remainder of 10 and when divided by 16, leaves a remainder of 11 = ?
115
235
247
475
Q.9
If three number are 2a, 5a and 7a, what will be their LCM ?
70a
65a
75a
73a
Q.10
Product of two co-prime numbers is 117. Then their LCM is = ?
117
9
13
39
Q.11
The least number which when increased by 5 is divisible by each one of 24, 32, 36 and 54 is = ?
427
859
869
4320
Q.12
Three sets of English , Mathematics and Science books containing 336, 240 and 96 books respectively have to be stacked in such a way that all the books are stored subject wise and the height of each stack is the same. Total number of stakes will be ?
14
21
22
48
Q.13
HCF of $$\frac{2}{3}{\text{,}}\frac{4}{5}$$ and $$\frac{6}{7}$$ is = ?
$$\frac{{48}}{{105}}$$
$$\frac{2}{{105}}$$
$$\frac{1}{{105}}$$
$$\frac{{24}}{{105}}$$
Q.14
The sum of two numbers is 45. Their difference is $$\frac{1}{9}$$ of their sum. Their LCM is = ?
100
150
200
250
Q.15
The number nearest to 43582 divisible by each of 25, 50 and 75 is = ?
43500
43550
43600
43650
Q.16
Six bells commence 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 ?
4
10
15
16
Q.17
Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
4
5
6
8
Q.18
When Seeta made necklaces of either 16 beads, 20 beads or 36 beads, not a single bead was left over. What could be the least number of beads Seeta had = ?
700
720
750
780
Q.19
What is the least natural number which leaves no remainders when divided by all the digits from 1 to 9 ?
1800
1920
2520
5040
Q.20
If x:y be the ratio of two whole numbers and z be their HCF, then the LCM of those two number is = ?
$$yz$$
$$\frac{{xz}}{y}$$
$$\frac{{xy}}{z}$$
$$xyz$$
Q.21
Find the least multiple of 23, which when divided by 18, 21 and 24 leaves remainders 7, 10 and 13 respectively = ?
3002
3013
3024
3036
Q.22
Find the greatest number of 4 digits which when divided by 4, 5, 6, 7 and 8 leaves 1, 2, 3, 4 and 5 as remainders = ?
9237
9240
9840
9999
Q.23
Let x be the smallest number, which when added to 2000 make the resulting number divisible by 12, 16, 18 and 21. The sum of the digits of x is = ?
6
5
7
8
Q.24
A general of an Army wants to create a formation of square from 36562 army men. After arrangement, he found some army men remainder unused.
36
65
81
97
Q.25
What is the greatest number of 3 digits which when divided by 6, 9 and 12 leaves a remainder of 3 in each case ?
903
939
975
996
Q.26
Five bells begin to toll together and toll respectively at intervals of 6, 7, 8, 9 and 12 seconds. After how many seconds will they toll together again ?
72 seconds
612 seconds
504 seconds
318 seconds
Q.27
The least number which when divided by 6, 9, 12, 15, 18 leaves the same remainder 2 in each case is = ?
180
176
182
178
Q.28
The LCM of three different numbers is 120. Which of the following cannot be their HCF?
8
12
24
35
Q.29
A farmer has 945 cows and 2475 sheep. He farms them into flocks, keeping cows and sheep separate and having the same number of animals in each flock. If these flocks are as large as possible, then the maximum number of animals in each flock and total number of flocks required for the purpose are respectively ?
15 and 228
9 and 380
45 and 76
46 and 75
Q.30
The greatest 4-digit number exactly divisible by 10, 15, 20 is = ?
9990
9960
9980
9995
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