Q.1 Find the HCF of 36 and 60.
6
12
18
24
Explanation - The factors of 36: 1,2,3,4,6,9,12,18,36; factors of 60: 1,2,3,4,5,6,10,12,15,20,30,60. The highest common factor is 12.
Correct answer is: 12
Q.2 Find the LCM of 8 and 12.
24
48
36
12
Explanation - Multiples of 8: 8,16,24,32...; multiples of 12: 12,24,36...; the smallest common multiple is 24.
Correct answer is: 24
Q.3 HCF of 45, 60, and 75 is:
5
10
15
20
Explanation - Factors: 45:1,3,5,9,15,45; 60:1,2,3,4,5,6,10,12,15,20,30,60; 75:1,3,5,15,25,75. Highest common factor is 15.
Correct answer is: 15
Q.4 LCM of 7 and 5 is:
12
35
25
40
Explanation - 7 and 5 are co-prime; LCM = 7*5 = 35.
Correct answer is: 35
Q.5 The HCF of 48 and 180 is:
12
24
36
6
Explanation - Factors of 48: 1,2,3,4,6,8,12,16,24,48; Factors of 180: 1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180; highest common factor is 12.
Correct answer is: 12
Q.6 The LCM of 15, 20, and 30 is:
60
90
120
30
Explanation - Multiples of 15:15,30,45,60...; 20:20,40,60...; 30:30,60...; smallest common multiple = 60.
Correct answer is: 60
Q.7 If HCF of two numbers is 8 and their LCM is 96, the product of numbers is:
384
768
512
640
Explanation - Product of two numbers = HCF * LCM = 8 * 96 = 768.
Correct answer is: 768
Q.8 Find the HCF of 81 and 153.
9
27
17
3
Explanation - Factors of 81:1,3,9,27,81; Factors of 153:1,3,9,17,51,153; highest common factor = 9.
Correct answer is: 9
Q.9 LCM of 9, 12, and 15 is:
180
60
45
90
Explanation - Prime factorization: 9=3^2, 12=2^2*3, 15=3*5; LCM = 2^2*3^2*5 = 180.
Correct answer is: 180
Q.10 The HCF of 56 and 72 is:
8
16
12
18
Explanation - Factors of 56:1,2,4,7,8,14,28,56; Factors of 72:1,2,3,4,6,8,9,12,18,24,36,72; HCF = 8.
Correct answer is: 8
Q.11 Two numbers are 18 and 24. Their LCM is:
72
36
48
60
Explanation - Multiples of 18:18,36,54,72...; multiples of 24:24,48,72...; LCM = 72.
Correct answer is: 72
Q.12 The HCF of 14, 28, and 42 is:
7
14
21
28
Explanation - Factors: 14:1,2,7,14; 28:1,2,4,7,14,28; 42:1,2,3,6,7,14,21,42; HCF = 14.
Correct answer is: 14
Q.13 LCM of 4, 6, and 8 is:
12
24
48
16
Explanation - Prime factorization: 4=2^2,6=2*3,8=2^3; LCM = 2^3*3=24.
Correct answer is: 24
Q.14 If HCF of 54 and 24 is 6, what is their LCM?
216
228
234
240
Explanation - LCM = (54*24)/HCF = 1296/6 = 216.
Correct answer is: 216
Q.15 HCF of 20 and 45 is:
5
10
15
20
Explanation - Factors of 20:1,2,4,5,10,20; factors of 45:1,3,5,9,15,45; HCF = 5.
Correct answer is: 5
Q.16 The LCM of 25 and 40 is:
100
200
300
400
Explanation - Prime factors: 25=5^2,40=2^3*5; LCM = 2^3*5^2 = 200.
Correct answer is: 200
Q.17 HCF of 81, 54, and 27 is:
9
18
27
3
Explanation - Factors of 27:1,3,9,27; 54:1,2,3,6,9,18,27,54; 81:1,3,9,27,81; HCF = 27.
Correct answer is: 27
Q.18 Find LCM of 16 and 20.
60
80
100
120
Explanation - Prime factors: 16=2^4,20=2^2*5; LCM = 2^4*5 = 80.
Correct answer is: 80
Q.19 Two numbers are 8 and 12. If their HCF is 4, what is their LCM?
16
24
32
48
Explanation - Product of numbers = 8*12=96; LCM = product/HCF = 96/4=24.
Correct answer is: 24
Q.20 The HCF of 32, 48, and 80 is:
8
16
24
32
Explanation - Factors of 32:1,2,4,8,16,32; 48:1,2,3,4,6,8,12,16,24,48; 80:1,2,4,5,8,10,16,20,40,80; HCF = 16.
Correct answer is: 16
Q.21 LCM of 18 and 24 is:
72
54
48
36
Explanation - Multiples of 18:18,36,54,72...; multiples of 24:24,48,72...; LCM = 72.
Correct answer is: 72
Q.22 The HCF of 100 and 125 is:
20
25
15
10
Explanation - Factors of 100:1,2,4,5,10,20,25,50,100; factors of 125:1,5,25,125; HCF = 25.
Correct answer is: 25
Q.23 Find LCM of 14 and 21.
42
28
56
36
Explanation - Multiples of 14:14,28,42...; multiples of 21:21,42...; LCM = 42.
Correct answer is: 42
Q.24 The HCF of 66 and 99 is:
11
33
22
44
Explanation - Factors of 66:1,2,3,6,11,22,33,66; factors of 99:1,3,9,11,33,99; HCF = 33.
Correct answer is: 33