Quantitative Aptitude · Mathematics
HCF and LCM
215 Questions
Improve your quantitative aptitude speed by solving these HCF and LCM questions. The problems involve finding the highest common factor and least common multiple for sets of numbers. These calculations form a core part of the mathematics section in SSC, banking, and railway recruitment exams.
Finding HCFFinding LCMGreatest common factorLeast common multipleNumber properties
HCF and LCM Questions
A
Correct answer
Explanation
Prime Factors of 16 = 2 x 2 x 2 x 2
Prime Factors of 22 = 2 x 11
Lowest common multiple = 24 x 11 = 176
B
Correct answer
Explanation
Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 118 = 1, 2, 59, 118
Common factors = 1 and 2
HCF of 96 and 118 = 2
C
Correct answer
Explanation
Multiples of 6 are 6, 12, 18, 24, 36, 42, 48, 54, 60....
Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90.......
Common multiples = 18, 36, 54
LCM of 6 and 9 is 18.
-
14, 12, 18
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16, 12, 14
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12, 18, 24
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18, 24, 28
C
Correct answer
Explanation
12, 18, 24
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84
Multiples of 18 = 18, 36, 54, 72, 90
Multiples of 24 = 24, 48, 72, 96
LCM of 12, 18, 24 = 72
-
(a + b)
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(a + b)2
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(a + b)3
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a - b
B
Correct answer
Explanation
Find LCM of (a+b)² and (a+b). Since (a+b)² = (a+b)(a+b), it's already a multiple of (a+b). The LCM of a quantity and its square is always the square itself. LCM = (a+b)².
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85 and 90
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75 and 60
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60 and 95
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76 and 62
B
Correct answer
Explanation
75 and 60
Factors of 75 = 75, 150, 225, 300, 375
Factors of 60 = 60, 120, 180, 240, 300, 360
LCM of 60 and 75 = 300
-
(p - q)
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pqr
-
pqr(p - q)
-
pq(p - q)
C
Correct answer
Explanation
Factors of pq (p - q) = p × q × (p - q)
Factors of pqr (p - q) = p × q × r × (p - q)
LCM = p × q × r (p - q)
-
(x + z) (x - z)
-
(x + z)2
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(x - z)2
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x - z
A
Correct answer
Explanation
Factors of (x2 - z2) = (x + z) (x - z)
Factors of (x + z) = (x + z)
LCM = (x + z) (x - z)
= (x2 - z2)
-
15 and 27
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27 and 61
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21 and 35
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15 and 21
D
Correct answer
Explanation
15 and 21
Factors of 15 = 3 × 5
Factors of 21 = 3 × 7
LCM = 3 × 5 × 7 = 105
-
84 and 32
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89 and 35
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84 and 36
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94 and 32
A
Correct answer
Explanation
Factors of 84 = 2 × 2 × 3 × 7
Factors of 32 = 2 × 2 × 2 × 2 × 2
LCM = 2 × 2 × 3 × 7 × 2 × 2 × 2 = 672
-
26, 24, 18
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28, 14, 21
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18, 34, 21
-
28, 34, 16
B
Correct answer
Explanation
Multiples of 28 = 28, 56, 84
Multiples of 14 = 14, 28, 42, 56, 70, 84, 98
Multiples of 21 = 21, 42, 63, 84
LCM = 84
-
4y2, 16x, 8y
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2y2, 16xy, 8a
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8y2, 16xy, 10y
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18y2, 16xy, 4y
C
Correct answer
Explanation
8y2, 16xy, 10y
Factors of 8y2 = 2 × 2 × 2 × y × y
Factors of 10y = 2 x 5 x y
Factors of 16 × y = 2 × 2 × 2 × 2 × x × y
LCM = 2 × 2 × 2 × 2 × 5 x x × y
= 80xy2
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10ab, 20ab, 28ab
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11ab, 21ab, 28ab
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12ab, 20ab, 14ab
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20ab, 26ab, 14ab
A
Correct answer
Explanation
10ab, 20ab, 28ab
Factors of 10ab = 2 × 5 × a × b
Factors of 20ab = 2 × 2 × 5 × a × b
Factors of 28ab = 2 × 2 × 7 × a × b
LCM = 140ab
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28b, 20ab3, 16b4
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28b, 20ab2, 16b4
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20b2, 28ab, 18b4
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28b4, 18ab3, 16b
A
Correct answer
Explanation
28b2, 20ab3, 16b4
Factors of 28b2 = 2 × 2 × 7 × b × b
Factors of 20ab3 = 2 × 2 × 5 × a × b × b × b
Factors of 16b4 = 2 x 2 x 2 x 2 x b x b x b x b
LCM = 2 × 2 × 7 × 5 × 2 × 2 × b × b × a × b × b = 560ab4
C
Correct answer
Explanation
Factors of 22 = 2 × 11
Factors of 54 = 2 × 3 × 3 × 3
Factors of 108 = 2 × 2 × 3 × 3 × 3
LCM = 2 × 11 × 3 × 3 × 3 × 2 × 3 × 3 × 3 = 1188