Mathematics - HCF and LCM

Exam Duration: 45 Mins Total Questions : 30

1 )

The H.C.F of \(2^{2}\times3^{3}\times5^{2}\),\(2^{3}\times3^{2}\times5^{2}\times7\) and \(2^{4}\times3^{4}\times5\times7^{2}\times11\) is :

(a)
\(2^{2}\times3^{2}\times5\)
(b)
\(2^{2}\times3^{2}\times5\times7\times11\)
(c)
\(2^{4}\times3^{4}\times5^{5}\)
(d)
\(2^{4}\times3^{4}\times5^{5}\times7\times11\)

2 )

The H.C.F of 204,1190 and 1445 is :

(a)
17
(b)
18
(c)
19
(d)
21

3 )

Which of the following is a pair of co-primes?

(a)
(16,62)
(b)
(18,25)
(c)
(21,35)
(d)
(23,92)

4 )

The H.C.F of 3556 and 3444 is :

(a)
23
(b)
25
(c)
26
(d)
28

5 )

The L.C.M of \(2^{3}\times3^{2}\times5\times11\),\(2^{4}\times3^{4}\times5^{2}\times7\)and \({ 2 }^{ 5 }\times { 3 }^{ 4 }\times { 5 }^{ 3 }\times { 7 }^{ 2 }\times 11\) is.

(a)
\(2^{3}\times3^{2}\times5\)
(b)
\(2^{5}\times3^{4}\times5^{3}\)
(c)
\(2^{3}\times3^{2}\times5\times7\times11\)
(d)
\(2^{5}\times3^{4}\times5^{3}\times7^{2}\times11\)

6 )

The L.C.M of 22,54,108,135 and 198 is:

(a)
330
(b)
1980
(c)
5940
(d)
11880

7 )

The L.C.M of 148 and 185 is :

(a)
680
(b)
740
(c)
2960
(d)
3700

8 )

The H.C.F of \({9\over10},{12\over25},{18\over35}\) and \(\frac { 21 }{ 40 } \) is

(a)
\(3\over5\)
(b)
\(252\over5\)
(c)
\(3\over2800\)
(d)
\(63\over700\)

9 )

The L.C.M of 3,2.7 and 0.09 is :

(a)
2.7
(b)
0.27
(c)
0.027
(d)
27

10 )

H.C.F of 3240,3600 and a third number is 36 and their L.C.M is \(2^{4}\times3^{5}\times5^{2}\times7^{2}\). The third number is :

(a)
\(2^{2}\times3^{5}\times7^{2}\)
(b)
\(2^{2}\times5^{3}\times7^{2}\)
(c)
\(2^{5}\times5^{2}\times7^{2}\)
(d)
\(2^{4}\times3^{5}\times5^{2}\times7^{2}\)

11 )

Three numbers are in the ratio 1:2:3 and their H.C.F is 12 .The numbers are:

(a)
4,8,12
(b)
5,10,15
(c)
10,20,30
(d)
12,24,36

12 )

The sum of two numbers is 216 and their H.C.F is 27 .The numbers are:

(a)
27,189
(b)
81,189
(c)
108,108
(d)
154,162

13 )

Three numbers are in the ratio of 3:4:5 and their L.C.M. is 2400.Their H.C.F is:

(a)
40
(b)
80
(c)
120
(d)
200

14 )

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 :

(a)
279
(b)
283
(c)
308
(d)
318

15 )

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 :

(a)
12
(b)
48
(c)
84
(d)
108

16 )

The product of the L.C.M and H.C.M of two numbers is 24. The difference of two numbers is 2.Find the numbers.

(a)
2 and 4
(b)
6 and 4
(c)
8 and 6
(d)
8 and 10

17 )

If the sum of two number is 55 and H.C.F. and L.C.M. of these numbers are 5 and 120 respectively,then the sum of the reciprocals of the numbers is equal to:

(a)
\(55\over601\)
(b)
\(601\over55\)
(c)
\(11\over120\)
(d)
\(120\over11\)

18 )

The HCF and LCM of two numbers are 50 and 250 respectively.If the first number is divided by 2,the quotient is 50 .The second number is :

(a)
50
(b)
100
(c)
125
(d)
250

19 )

The product of two numbers is 1320 and their HCF is 6 .The LCM of the numbers is :

(a)
220
(b)
1314
(c)
1326
(d)
7920

20 )

The LCM of three different numbers is 120.Which of the following cannot be their HCF?

(a)
8
(b)
12
(c)
24
(d)
35

21 )

About the number of pairs which have 16 as their HCF and 136 as their LCM..,we can definitely say that:

(a)
no such pair exists
(b)
only one such pair exists
(c)
only two such pairs exists
(d)
many such pairs exists

22 )

LCM of two prime numbers x and y (x>y) is 161.The value of 3y-x is :

(a)
-2
(b)
-1
(c)
1
(d)
2

23 )

A rectangular courtyard 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles,all of the same size.What is the largest size of the tiles which could be used for the purpose ?

(a)
14 cms
(b)
21 cms
(c)
42 cms
(d)
None of these

24 )

The greatest number which can divide 1356,1868 and 2764 leaving the same remainder 12 in each case is :

(a)
64
(b)
124
(c)
156
(d)
260

25 )

Which of the following fractions is the largest?

(a)
\(7\over8\)
(b)
\(13\over16\)
(c)
\(31\over40\)
(d)
\(63\over80\)

26 )

What will be the least number which when doubled will be exactly divisible by 12,18,21 and 30?

(a)
196
(b)
630
(c)
1260
(d)
2520

27 )

The least number which should be added to 2497 so that the sum is exactly divisible by 5,6,4 and 3 is :

(a)
3
(b)
13
(c)
23
(d)
33

28 )

The least number which is a perfect square and is divisible by each of the numbers 16,20 and 24 is :

(a)
1600
(b)
3600
(c)
6400
(d)
14400

29 )

Find the least multiple of 23,which divided by 18,21 and 24 leaves remainders 7,10 and 13 respectively.

(a)
3002
(b)
3013
(c)
3024
(d)
3036

30 )

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?