Q.1 Find the HCF of 48 and 180.
12
24
36
18
Explanation - The prime factors of 48 are 2^4 * 3, and of 180 are 2^2 * 3^2 * 5. Common factors are 2^2 * 3 = 12.
Correct answer is: 12
Q.2 Find the LCM of 6 and 15.
30
45
60
90
Explanation - Prime factors: 6 = 2*3, 15 = 3*5. LCM = 2*3*5 = 30.
Correct answer is: 30
Q.3 If HCF of two numbers is 8 and their LCM is 96, and one number is 24, find the other number.
32
40
48
56
Explanation - Product of numbers = HCF * LCM = 8 * 96 = 768. Other number = 768 / 24 = 32.
Correct answer is: 32
Q.4 Find HCF of 84, 126, and 210.
14
21
42
28
Explanation - Prime factors: 84 = 2^2 * 3 * 7, 126 = 2 * 3^2 * 7, 210 = 2 * 3 * 5 * 7. Common factors: 2*3*7 = 42.
Correct answer is: 42
Q.5 Find the LCM of 12, 15, and 20.
60
120
180
240
Explanation - Prime factors: 12 = 2^2*3, 15 = 3*5, 20 = 2^2*5. LCM = 2^2*3*5 = 60.
Correct answer is: 60
Q.6 Two numbers are 16 and 24. Find their HCF and LCM.
HCF=4, LCM=96
HCF=8, LCM=48
HCF=6, LCM=64
HCF=8, LCM=32
Explanation - HCF of 16 and 24 = 8, LCM = (16*24)/8 = 48.
Correct answer is: HCF=8, LCM=48
Q.7 HCF of two numbers is 15 and LCM is 180. If one number is 45, find the other number.
50
60
75
45
Explanation - Product = 15*180 = 2700. Other number = 2700 / 45 = 60.
Correct answer is: 60
Q.8 Find the LCM of 7, 14, and 21.
42
84
126
28
Explanation - LCM = highest powers of prime factors: 7*2*3 = 42.
Correct answer is: 42
Q.9 The HCF of 108 and 180 is?
12
36
18
24
Explanation - Prime factors: 108 = 2^2*3^3, 180 = 2^2*3^2*5. HCF = 2^2*3^2 = 36.
Correct answer is: 36
Q.10 Two numbers are in the ratio 4:5. Their HCF is 6. Find the numbers.
24, 30
12, 15
18, 24
20, 25
Explanation - Numbers = 6*4 = 24, 6*5 = 30.
Correct answer is: 24, 30
Q.11 Find the HCF of 225 and 315.
15
25
45
35
Explanation - Prime factors: 225 = 3^2*5^2, 315 = 3^2*5*7. HCF = 3^2*5 = 45.
Correct answer is: 45
Q.12 The LCM of two numbers is 2520 and one number is 180. If HCF is 12, find the other number.
168
1680
144
210
Explanation - Product = HCF*LCM = 12*2520 = 30240. Other number = 30240 / 180 = 168.
Correct answer is: 168
Q.13 Find HCF of 36, 60, and 84.
6
12
18
24
Explanation - Prime factors: 36=2^2*3^2, 60=2^2*3*5, 84=2^2*3*7. HCF = 2^2*3=12.
Correct answer is: 12
Q.14 Two numbers are 56 and 98. Find their LCM.
392
196
784
448
Explanation - LCM = (56*98)/HCF. HCF = 14, so LCM = (56*98)/14 = 392.
Correct answer is: 392
Q.15 If LCM of 8, 12 and 20 is x, then x is?
60
120
240
180
Explanation - LCM = 2^2*3*5 = 120.
Correct answer is: 120
Q.16 HCF of 270 and 360 is?
30
45
90
60
Explanation - Prime factors: 270 = 2*3^3*5, 360 = 2^3*3^2*5. HCF = 2*3^2*5 = 90.
Correct answer is: 90
Q.17 Find the HCF of 120 and 144 using Euclid’s method.
12
24
6
36
Explanation - Subtract smaller from larger repeatedly or use division method: HCF = 24.
Correct answer is: 24
Q.18 Two numbers are 45 and 60. If HCF is 15, find their LCM.
120
180
150
225
Explanation - LCM = (45*60)/15 = 180.
Correct answer is: 180
Q.19 The LCM of two numbers is 72 and their HCF is 6. If one number is 18, find the other.
24
36
12
30
Explanation - Other number = (LCM*HCF)/given number = (72*6)/18 = 24.
Correct answer is: 24
Q.20 Find HCF of 144, 192, and 240.
24
48
36
12
Explanation - Prime factors: 144=2^4*3^2, 192=2^6*3, 240=2^4*3*5. HCF=2^4*3=48.
Correct answer is: 48
Q.21 The LCM of 9, 12, and 15 is?
180
60
90
120
Explanation - LCM = 3^2 * 2^2 * 5 = 180.
Correct answer is: 180
Q.22 Find HCF of 81 and 153.
9
27
17
3
Explanation - Prime factors: 81=3^4, 153=3^2*17. HCF = 3^2=9.
Correct answer is: 9
Q.23 Two numbers are 72 and 120. Find their HCF and LCM.
HCF=24, LCM=360
HCF=12, LCM=720
HCF=18, LCM=480
HCF=24, LCM=480
Explanation - HCF = 24, LCM = (72*120)/24 = 360.
Correct answer is: HCF=24, LCM=360
Q.24 If HCF of two numbers is 7 and one number is 49, find the smallest possible LCM.
49
56
63
98
Explanation - For minimum LCM, numbers = HCF and multiple of HCF. So other number = 7 => LCM = 49.
Correct answer is: 49