HCF and LCM – Railway Maths Part II

Total Questions: 50

11. Find the HCF of (a³ + b³), (a + b)² and (a² − b²). [RRB JE 31/05/2019 (Evening)]

Correct Answer: (a) (a + b)
Solution:

We know that

12. The HCF of two numbers is 7 and their LCM is 434. If one of the numbers is 14, find the other. [Group D 17/08/2022 (Evening)]

Correct Answer: (b) 217
Solution:

13. The HCF of 108 and 144 is: [Group D 18/08/2022 (Evening)]

Correct Answer: (a) 36
Solution:

108 = 3 × 4 × 9
144 = 4 × 4 × 9
H.C.F of 108 and 144 = 4 × 9 = 36

14. Two numbers are in the ratio 5 : 7. If their HCF is 17, then find the numbers. [Group D 22/08/2022 (Morning)]

Correct Answer: (a) 85, 119
Solution:

Numbers = 17 × 5 and 17 × 7
= 85, 119

15. The product of two numbers is 1472 and their HCF is 8. Find their LCM. [Group D 22/08/2022 (Evening)]

Correct Answer: (c) 184
Solution:

16. The HCF of 45, 78 and 117 is: [Group D 23/08/2022 (Morning)]

Correct Answer: (d) 3
Solution:

45 = 3 × 3 × 5
78 = 2 × 3 × 13
117 = 3 × 3 × 13
H.C.F of 45, 78 and 117 = 3

17. Find the least number which when added to 2488, then number obtained will be completely divisible by 3, 4, 5 and 6. [Group D 23/08/2022 (Evening)]

Correct Answer: (d) 32
Solution:

18. Find the least six-digit number that is exactly divisible by 8, 10, 12 and 16. [Group D 24/08/2022 (Evening)]

Correct Answer: (d) 100080
Solution:

19. What is the least 5-digit number, which when divided by 15, 24, 35 and 42, the remainder in each case is 13? [Group D 25/08/2022 (Morning)]

Correct Answer: (c) 10093
Solution:

Smallest 5- digit number = 10000
L.C.M of 15, 24, 35, 42 = 840
840 - 760 = 80 + 13 = 93
Required number = 10000 + 93 = 10093

20. The sum of two positive integers is 55. If their HCF and LCM are 5 and 120, respectively, then the sum of their reciprocals is .......... [Group D 25/08/2022 (Morning)]

Correct Answer: (b) 11/120
Solution:

Let the Two number are x and y.
Product of the two numbers (xy)
= L.C.M × H.C.F = 5 × 120 = 600
Sum of their reciprocals