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HCF and LCM
📆 June 13, 2025
Total Questions: 50
21.
If r is the remainder when each of 6454, 7306 and 8797 is divided by the greatest number d (d > 1) then (d - r) is:
[SSC CPO 13/12/2019 (Morning)]
(a) 126
(b) 64
(c) 137
(d) 149
Correct Answer:
(d) 149
22.
In finding the HCF of two numbers by division method, the quotients are 1, 8 and 2 respectively, and the last divisor is 105, what is the sum of the numbers ?
[SSC CPO 11/12/2019 (Evening)]
(a) 3570
(b) 3885
(c) 3780
(d) 3675
Correct Answer:
(c) 3780
23.
When the smallest number x is divided by 5, 6, 8, 9 and 12, it gives remainder 1 in each case. But x is divisible by 13. What will be the remainder when x will be divided by 31
[SSC MTS 20/08/2019 (Afternoon)]
(a) 1
(b) 5
(c) 3
(d) 0
Correct Answer:
(b) 5
24.
The Highest Common Factor and Lowest Common Multiple of two numbers p and q are A and B respectively. IF A + B = p + q then the value of A³ + B³ is:
[SSC MTS 09/08/2019 (Evening)]
(a) p
(b) q³
(c) p³ + q³
(d) p³ - q³
Correct Answer:
(c) p³ + q³
25.
What is the largest number that divides 460, 491 and 553 and leaves the remainder 26 in each case?
[SSC MTS 06/08/2019 (Afternoon)]
(a) 27
(b) 35
(c) 33
(d) 31
Correct Answer:
(d) 31
26.
A is the smallest three-digit number which when divided by 3, 4 and 5 gives remainder 1, 2 and 3 respectively. What is the sum of the digits of A?
[SSC MTS 05/08/2019 (Afternoon)]
(a) 11
(b) 10
(c) 6
(d) 8
Correct Answer:
(b) 10
27.
The product of two numbers is 6760 and their HCF is 13. How many such pairs of numbers can be formed?
[SSC CPO 16/03/2019 (Evening)]
(a) 2
(b) 3
(c) 1
(d) 4
Correct Answer:
(a) 2
28.
An oil merchant has 3 varieties of oil of volumes 432, 594 and 702 respectively. The number of cans of equal size that would be required to fill the oil separately is:
[SSC CPO 16/03/2019 (Afternoon)]
(a) 13, 15, 17
(b) 8, 11, 13
(c) 8, 13, 15
(d) 6, 9, 11
Correct Answer:
(b) 8, 11, 13
29.
Which of the following statements is true?
[SSC CPO 14/03/2019 (Morning)]
(a) LCM of two natural numbers is divisible by their HCF.
(b) HCF + LCM of two numbers = Product of the two numbers.
(c) Two prime numbers are co-prime numbers if their LCM is 1.
(d) HCF of two numbers is the smallest common divisor of both numbers.
Correct Answer:
(a) LCM of two natural numbers is divisible by their HCF.
30.
A milk vendor has 75 litres of cow milk, 45 litres of toned milk and 30 litres of full cream milk. These should be placed in different trays such that each tray contains the same quantity of milk and two kinds of milk should not be mixed in a tray. What is the least number of trays required to place all the milk?
[SSC CHSL Tier II (18/11/2024)]
(a) 15
(b) 25
(c) 10
(d) 20
Correct Answer:
(c) 10
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