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HCF and LCM
📆 June 13, 2025
Total Questions: 50
11.
There is a circular path around a sports field. Rahul takes 15 minutes to drive one round of the field, while Anil takes 18 minutes for the same. Suppose they both start from the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
[SSC MTS 11/05/2023 (Afternoon)]
(a) 120
(b) 100
(c) 80
(d) 90
Correct Answer:
(d) 90
12.
Let x = 224 and, y = 322 If the highest common factor of 23x and a × y is divisible by x and y, then what can be the possible value of a?
[SSC CPO 11/11/2022 (Evening)]
(a) 16
(b) 8
(c) 12
(d) 4
Correct Answer:
(a) 16
13.
The highest common factor of 108, 72 and 5a is a. What can be the least common multiple of 108, 72 and a ?
[SSC CPO 10/11/2022 (Afternoon)]
(a) 432
(b) 324
(c) 108
(d) 216
Correct Answer:
(d) 216
14.
What is the greatest positive integer that divides 554, 714 and 213 leaving the remainder 43, 57 and 67, respectively?
[SSC CPO 10/11/2022 (Afternoon)]
(a) 95
(b) 71
(c) 83
(d) 73
Correct Answer:
(d) 73
15.
Find the HCF of (4³¹⁵ - 1) and (4²⁵ - 1).
[SSC MTS 26/07/2022 (Morning)]
(a) 1
(b) (4²⁵- 1)
(c) 1024
(d) 1023
Correct Answer:
(d) 1023
16.
120 apples, 240 oranges and 150 pears are packed in cartons in such a way that each carton has the same number of fruits, each carton contains only one type of fruit and fruit is left unpacked. What is the smallest possible number of cartons needed for the purpose?
[SSC MTS 08/07/2022 (Evening)]
(a) 50
(b) 40
(c) 17
(d) 30
Correct Answer:
(c) 17
17.
The traffic lights at 3 different road crossings change after every 48 sec, 72 sec and 108 sec, respectively. If they all change simentionusly at 8: 20 a.m., then at what will they next change again simultaneously?
[SSC MTS 07/07/2022 (Morning)]
(a) 8 : 27 : 12 a.m.
(b) 8 : 33 : 32 a.m.
(c) 8:12:18 a.m.
(d) 8 : 40 : 14 a.m.
Correct Answer:
(a) 8 : 27 : 12 a.m.
18.
A and B are two prime numbers such that A > B and their LCM is 209. The value of A² - B is?
[SSC CGL 12/04/2022 (Evening)]
(a) 350
(b) 372
(c) 361
(d) 339
Correct Answer:
(a) 350
19.
13, a, b, c are four distinct numbers and the HCF of each pair of numbers (13, a): (13, b): (13, c) is 13, where a, b, c are each less than 60 and abc. What is the value of (a + c)/b ?
[SSC CGL 13/04/2021 (Morning)]
(a) 3.5
(b) 2
(c) 5
(d) 4.5
Correct Answer:
(b) 2
20.
The sum of two numbers is 1215 and their HCF is 81. If the numbers lie between 500 and 700, then the sum of reciprocals of the numbers is
[SSC CPO 13/12/2019 (Evening)]
(a)
(b)
(c)
(d)
Correct Answer:
(a)
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