1. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
A. 9000
B. 9400
C. 9600
D. 9800
Explanation
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
2. The G.C.D. of 1.08, 0.36 and 0.9 is:
A. 0.03
B. 0.9
C. 0.18
D. 0.108
Explanation
Given numbers are 1.08, 0.36 and 0.90.
H.C.F. of 108, 36 and 90 is 18,
H.C.F. of given numbers = 0.18.
3.Find the lowest common multiple of 24, 36 and 40.
A. 120
B. 240
C. 360
D. 480
Explanation
2 | 24 - 36 - 40
--------------------
2 | 12 - 18 - 20
--------------------
2 | 6 - 9 - 10
-------------------
3 | 3 - 9 - 5
-------------------
| 1 - 3 - 5
L.C.M. = 2 x 2 x 2 x 3 x 3 x 5 = 360.
4.Find the HCF of 1365,1560 and 1755
Explanation:
1365=3*5*7*13
1560=2*2*2*3*5*13
1755=3*3*3*5*13
HCF=3*5*13=195
Alternate method
1560-1365=195
1755-1560=195
HCF= 195
5.The least number, which when divided by 48, 60, 72, 108 and 140 leaves
38, 50, 62, 98 and 130 as remainders respectively, is :
Solution :
(48 - 38 ) = ( 60 - 50 ) = ( 72 - 62 ) = ( 108 - 98 ) = ( 140 - 130 )
= 10 in every case
Leat number will be LCM of ( 48, 60, 72, 108, 140 ) - 10
LCM = 15120
So, required number = 15120 - 10 = 15110
6.The traffic lights at three different road crossings change after every 24, 36 and 48 secs respectively. If they all change simultaneously at 09 : 10 : 00 hours , then at what time will they again change simultaneously ?
Solution :
Here time requirement is least so we will find LCM
Change interval will be LCM of 24, 36, 48 = 144 sec
144 sec= 2 min 24 sec,
So interval of change will be at 09 : 12 : 24 hours
7. If the sum of two numbers is 55 and the 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) 55/601
b) 601/55
c) 11/120 d) 120/11
Explanation
Let the numbers be a and b. Then, a + b = 55 and ab = 5 x 120 = 600.
The required sum =(1/a)+(1/b)=(a+b)/ab
=55/600 = 11/120
8. The L.C.M. of two numbers is 4800 and their G.C.M. is 160. If one of the numbers is 480, then the other number is:
a) 1600
b) 1800
c) 2200
d) 2600
e) None of these
Explanation:
Let n be the required number.
Since, HCF x LCM = product of two numbers.
=>4800 x 160 = 480 x n.
=>n=(4800 x 160)/480.
=>n=1600.
9.The L.C.M. of two numbers is 140. If their ratio is 2:5, then the numbers are:
a) 28,70
b) 28,7
c) 8,70
d) 8,40
e) None of these
Explanation:
LCM.=140
let HCF be x
Then the 2 nos. all be 2x & 5x
Then product of 2nos. = LCM * HCF
2x*5x= 140
10x =14x
x= 14
2nos. 2*14 &/5*14
Ans: 28,70
10. The product of two numbers is 16200. If their LCM is 216, find their HCF.
a) 75
b) 70
c) 80
d) Data inconsistent
Solution:
216*HCF =16200
HCF=75
11..M and N are two distinct natural numbers. HCF and LCM of M and N are K and L respectively. A is also a natural number, which of the following relations is not possible?
a) K*L=A
b) K*A=L
c) L*A=K
d) None of these
Solution:
L*A=K
12. The ratio of two numbers is 3:4 and their HCF is 4.Their LCM is:
a) 12
b) 16
c) 24
d) 48
Solution:
Let the numbers be 3x and 4x.
Then,their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
13. 7.What will be obtained if 8 is subtracted from the HCF of 168, 189, and 231?
a) 15
b) 10
c) 21
d) None of these
Solution:
HCF=(189-168),(231-189),(231-168)
=(21,42,63)=21
=21-8
=14
14. The least square number which divides 8, 12 and 18 is?
A) 100
B) 121
C) 64
D) 144
Solution:
LCM = 72 72 * 2
= 144
15. The least number which when diminished by 7 is divisible by 21, 28, 36 and 45 is?
A) 1267
B) 1265
C) 1261
D) 68
Solution:
LCM = 1260 1260 + 7
= 1267
16. 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?
A) 246 seconds
B) 242 seconds
C) 240 seconds
D) 243 seconds
Solution:
LCM = 240
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.
A) 51
B) 61
C) 47
D) 45
Solution:
HCF of 435, 493, 551
= 29 (453/29) + (493/29) + (551/29)
= 51
A. 9000
B. 9400
C. 9600
D. 9800
Explanation
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
2. The G.C.D. of 1.08, 0.36 and 0.9 is:
A. 0.03
B. 0.9
C. 0.18
D. 0.108
Explanation
Given numbers are 1.08, 0.36 and 0.90.
H.C.F. of 108, 36 and 90 is 18,
H.C.F. of given numbers = 0.18.
3.Find the lowest common multiple of 24, 36 and 40.
A. 120
B. 240
C. 360
D. 480
Explanation
2 | 24 - 36 - 40
--------------------
2 | 12 - 18 - 20
--------------------
2 | 6 - 9 - 10
-------------------
3 | 3 - 9 - 5
-------------------
| 1 - 3 - 5
L.C.M. = 2 x 2 x 2 x 3 x 3 x 5 = 360.
4.Find the HCF of 1365,1560 and 1755
Explanation:
1365=3*5*7*13
1560=2*2*2*3*5*13
1755=3*3*3*5*13
HCF=3*5*13=195
Alternate method
1560-1365=195
1755-1560=195
HCF= 195
5.The least number, which when divided by 48, 60, 72, 108 and 140 leaves
38, 50, 62, 98 and 130 as remainders respectively, is :
Solution :
(48 - 38 ) = ( 60 - 50 ) = ( 72 - 62 ) = ( 108 - 98 ) = ( 140 - 130 )
= 10 in every case
Leat number will be LCM of ( 48, 60, 72, 108, 140 ) - 10
LCM = 15120
So, required number = 15120 - 10 = 15110
6.The traffic lights at three different road crossings change after every 24, 36 and 48 secs respectively. If they all change simultaneously at 09 : 10 : 00 hours , then at what time will they again change simultaneously ?
Solution :
Here time requirement is least so we will find LCM
Change interval will be LCM of 24, 36, 48 = 144 sec
144 sec= 2 min 24 sec,
So interval of change will be at 09 : 12 : 24 hours
7. If the sum of two numbers is 55 and the 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) 55/601
b) 601/55
c) 11/120 d) 120/11
Explanation
Let the numbers be a and b. Then, a + b = 55 and ab = 5 x 120 = 600.
The required sum =(1/a)+(1/b)=(a+b)/ab
=55/600 = 11/120
8. The L.C.M. of two numbers is 4800 and their G.C.M. is 160. If one of the numbers is 480, then the other number is:
a) 1600
b) 1800
c) 2200
d) 2600
e) None of these
Explanation:
Let n be the required number.
Since, HCF x LCM = product of two numbers.
=>4800 x 160 = 480 x n.
=>n=(4800 x 160)/480.
=>n=1600.
9.The L.C.M. of two numbers is 140. If their ratio is 2:5, then the numbers are:
a) 28,70
b) 28,7
c) 8,70
d) 8,40
e) None of these
Explanation:
LCM.=140
let HCF be x
Then the 2 nos. all be 2x & 5x
Then product of 2nos. = LCM * HCF
2x*5x= 140
10x =14x
x= 14
2nos. 2*14 &/5*14
Ans: 28,70
10. The product of two numbers is 16200. If their LCM is 216, find their HCF.
a) 75
b) 70
c) 80
d) Data inconsistent
Solution:
216*HCF =16200
HCF=75
11..M and N are two distinct natural numbers. HCF and LCM of M and N are K and L respectively. A is also a natural number, which of the following relations is not possible?
a) K*L=A
b) K*A=L
c) L*A=K
d) None of these
Solution:
L*A=K
12. The ratio of two numbers is 3:4 and their HCF is 4.Their LCM is:
a) 12
b) 16
c) 24
d) 48
Solution:
Let the numbers be 3x and 4x.
Then,their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
13. 7.What will be obtained if 8 is subtracted from the HCF of 168, 189, and 231?
a) 15
b) 10
c) 21
d) None of these
Solution:
HCF=(189-168),(231-189),(231-168)
=(21,42,63)=21
=21-8
=14
14. The least square number which divides 8, 12 and 18 is?
A) 100
B) 121
C) 64
D) 144
Solution:
LCM = 72 72 * 2
= 144
15. The least number which when diminished by 7 is divisible by 21, 28, 36 and 45 is?
A) 1267
B) 1265
C) 1261
D) 68
Solution:
LCM = 1260 1260 + 7
= 1267
16. 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?
A) 246 seconds
B) 242 seconds
C) 240 seconds
D) 243 seconds
Solution:
LCM = 240
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.
A) 51
B) 61
C) 47
D) 45
Solution:
HCF of 435, 493, 551
= 29 (453/29) + (493/29) + (551/29)
= 51
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