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HCF and LCM
📆 June 13, 2025
Total Questions: 50
1.
The LCM of x² - 8x + 15 and x² - 5x + 6 is :
[SSC CPO 05/10/2023 (2nd Shift)]
(a) (x + 5)(x + 2)(x + 3)
(b) (x - 5)(x - 2)(x - 3)
(c) (x + 5)(x - 2)(x - 3)
(d) (x - 2)(x - 3)²(x - 5)
Correct Answer:
(b) (x - 5)(x - 2)(x - 3)
Solution:
2.
The greatest possible length that can be used to measure exactly the lengths of 3 m 15 cm, 5 m, and 6 m 85 cm is:
[SSC CPO 05/10/2023 (2nd Shift)]
(a) 11 cm
(b) 7 cm
(c) 9 cm
(d) 5 cm
Correct Answer:
(d) 5 cm
Solution:
3.
What is the HCF of (x⁶ + 1) and (x⁴ - 1)
[SSC CPO 05/10/2023 (1st Shift)]
(a) (1 + x²)
(b) (1 + x)
(c) 1
(d) (1 - x²)
Correct Answer:
(a) (1 + x²)
Solution:
4.
The LCM of two prime numbers x and y (x > y) is 533. The value of 4y - x is:
[SSC CPO 03/10/2023 (3rd Shift)]
(a) 11
(b) 21
(c) 18
(d) 23
Correct Answer:
(a) 11
Solution:
5.
What is the HCF of the polynomials (x³ - 8) (x³ -6x + 12x - 8) and (x³ - 4x² + 4x) ?
[SSC MTS 12/09/2023 (3rd Shift)]
(a) (x - 1)
(b) (x - 2)
(c) (x - 8)
(d) (x - 4)
Correct Answer:
(b) (x - 2)
Solution:
6.
Radha, Pratima and Reena begin to jog around a circular path and they complete their revolutions in 50 seconds, 75 seconds and 100 seconds, respectively. After how much time (in minutes) will they meet together at the starting point for the first time?
[ SSC MTS 11/09/2023 (3rd Shift)]
(a) 6
(b) 5
(c) 4
(d) 3
Correct Answer:
(b) 5
7.
Sanjay wants to exactly measure the lengths 7000 mm, 3850 mm and 12950 mm using a single measuring tape. What will be the greatest possible length (in cm) of the measuring tape?
[SSC MTS 11/09/2023 (2nd Shift)]
(a) 40
(b) 45
(c) 35
(d) 30
Correct Answer:
(c) 35
8.
Two tankers contain 850 litres and 680 litres of oil. Find the maximum capacity of a container which can measure the oil of both tankers when used, an exact number of times.
[SSC MTS 06/09/2023 (2nd Shift)]
(a) 425 litres
(b) 680 litres
(c) 340 litres
(d) 170 litres
Correct Answer:
(d) 170 litres
9.
Find the greatest two digit number which on dividing 219, 365, 511 leaves the remainders 3, 5, 7, respectively.
[SSC MTS 01/09/2023 (3rd Shift)]
(a) 63
(b) 82
(c) 53
(d) 72
Correct Answer:
(d) 72
10.
Five bells commence tolling together and toll at intervals of 5, 10, 15, 20 and 25 seconds respectively. In 1 hour 20 minutes, how many times do they toll together?
[SSC MTS 17/05/2023 (Afternoon)]
(a) 20
(b) 15
(c) 14
(d) 17
Correct Answer:
(d) 17
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