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Arithmetic Ability
Problems On H.C.F And L.C.M
Quiz 1
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Q.1
The LCM of two numbers is 12 times their HCF. The sum of the HCF and LCM is 403. If one of the number is 93, then the other is = ?
116
124
112
120
Q.2
The number of pairs of positive integers whose sum is 99 and HCF is 9 is = ?
5
2
3
4
Q.3
Find the HCF of $$\frac{3}{4}{\text{,}}\,\frac{5}{6}$$ and $$\frac{6}{7}$$ = ?
$$\frac{5}{{14}}$$
$$\frac{1}{{84}}$$
$$\frac{1}{{63}}$$
$$\frac{1}{{168}}$$
Q.4
The product of two whole numbers is 1500 and their HCF is 10. Find the LCM = ?
15000
150
1500
15
Q.5
The HCF and LCM of two numbers are 21 and 84 respectively. If the ratio of the two numbers is 1 : 4 then larger of the two numbers is = ?
48
12
84
108
Q.6
The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
3
13
23
33
Q.7
The product of two numbers is 2008 and their HCF is 13. The number of such pairs is = ?
1
2
3
4
Q.8
The ratio of two numbers is 3 : 4 and their LCM is 120. The sum of numbers is = ?
70
140
35
105
Q.9
The greatest 4 digit number which is exactly divisible by each one of the numbers 12, 18, 21 and 28 = ?
9288
9882
9828
9928
Q.10
The traffic lights at three different signal points change after every 45 seconds, 75 seconds and 90 seconds respectively. If all change simultaneously at 7:20:15 hours, then they will change again simultaneously at = ?
7:28:00 hours
7:27:45 hours
7:27:30 hours
7:27:50 hours
Q.11
LCM of two prime numbers x and y (x > y) is 161. Then the value of 3y - x is = ?
-2
-1
1
2
Q.12
The LCM and ratio of four numbers are 630 and 2 : 3 : 5 : 7 respectively. The difference between the greatest and least numbers is = ?
6
14
15
21
Q.13
The number nearest to 10000, which is exactly divisible by each of 3, 4, 5, 6, 7 and 8 is = ?
9240
10080
9996
10000
Q.14
The sum of two numbers is 528 and their HCF is 33. The number of pairs of numbers satisfying the above conditions is = ?
4
6
8
12
Q.15
A number x is divided by 7. When this number is divided by 8, 12 and 16. It leaves a remainder 3 in each case. The least value of x is = ?
148
149
150
147
Q.16
The smallest square number divisible by 10, 16 and 24 is ?
900
1600
2500
3600
Q.17
The least perfect square which is divisible by each of 21, 36 and 66 is = ?
214344
214434
213444
231444
Q.18
The HCF and LCM of two 2-digit number are 16 and 480 respectively. The numbers are ?
40, 48
60, 72
64, 80
80, 96
Q.19
A number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, and when divided by 8 leaves a remainder of 7, is = ?
1539
539
359
1359
Q.20
HCF and LCM of two numbers are 7 and 140 respectively. If the numbers are between 20 and 45, the sum of the numbers is = ?
70
77
63
56
Q.21
Two pipes of length 1.5 m and 1.2 m are to be cut into equal pieces without leaving any extra length of pipes. The greatest length of the pipe pieces of same size which can be cut from these two lengths will be = ?
0.13 m
26 m
0.3 m
0.41 m
Q.22
A milkman has 75 litres milk in one cane and 45 litres in another. The maximum capacity of container which can measure milk of either container exact number ?
1 litre
5 litres
15 litres
25 litres
Q.23
The G.C.D. (greatest common divisor) of 1.08, 0.36, 0.9 is = ?
0.03
0.9
0.18
0.108
Q.24
HCF of 3240, 3600, and a third number is 36 and their LCM is 2
4
× 3
5
× 5
2
× 7
2
. The third number is = ?
2
2
× 3
5
× 7
2
2
2
× 5
3
× 7
2
2
5
× 5
2
× 7
2
2
3
× 3
5
× 7
2
Q.25
The H.C.F. of $$\frac{a}{b}{\text{,}}\frac{c}{d}{\text{,}}\frac{e}{f}$$ is equal to = ?
$$\frac{{{\text{LCM of }}a,c,e{\text{ }}}}{{{\text{HCF of }}b,d.f}}$$
$$\frac{{{\text{HCF of }}a,c,e{\text{ }}}}{{{\text{LCM of }}b,d,f{\text{ }}}}$$
$$\frac{{{\text{HCF of }}a,c,e}}{{{\text{HCF of }}b,d.f}}$$
$$\frac{{ace}}{{bdf}}$$
Q.26
The HCF of $$\frac{9}{{10}}{\text{,}}\frac{{12}}{{25}}{\text{,}}\frac{{18}}{{35}}$$ and $$\frac{{21}}{{40}}$$ is = ?
$$\frac{3}{5}$$
$$\frac{{252}}{5}$$
$$\frac{3}{{1400}}$$
$$\frac{{63}}{{700}}$$
Q.27
The H.C.F of 2
4
× 3
2
× 5
3
× 7, 2
3
× 3
3
× 5
2
× 7
2
and 3 × 5 × 7 × 11 is = ?
105
1155
2310
27720
Q.28
The HCF and LCM of two numbers are 12 and 336 respectively. If one of the numbers is 84, the other is = ?
36
48
72
96
Q.29
The least number which when divided by 4, 6, 8 and 9 leave zero remainder in each case and when divided by 13 leaves a remainder of 7 is = ?
144
72
36
85
Q.30
The ratio of two numbers is 13 : 15 and their LCM is 39780 . The numbers are = ?
884, 1020
884, 1040
670, 1340
2652, 3060
0 h : 0 m : 1 s
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