HCF and LCM – Railway Maths Part Ⅴ

Total Questions: 48

41. The LCM of two numbers is 96 and their HCF is 8. If one of the two numbers is 32, then what is the other number? [RRB NTPC 08/02/2021 (Evening)]

Correct Answer: (d) 24
Solution:

Product of two numbers = HCF × LCM
⇒ 32 × 2nd number = 8 × 96
⇒ 2nd number = (8 × 96) / 32 = 24

42. The product of the LCM and HCF of two positive numbers is 36. The difference of the two numbers is 5. Find the numbers. [RRB NTPC 09/02/2021 (Evening)]

Correct Answer: (c) 4 and 9
Solution:

Product of two numbers = HCF × LCM = 36
Let the numbers be a and b
ab = 36
And a − b = 5 ⇒ a = 5 + b
Put the value of ‘a’ in the first equation
(5 + b) b = 36 = 9 × 4
On comparing both sides, we get
b = 4
a = 5 + 4 = 9

43. The LCM of two numbers is 26 times their HCF. The sum of the HCF and LCM is 729. If one number is 81. Find the other. [RRB NTPC 09/02/2021 (Evening)]

Correct Answer: (c) 234
Solution:

Let the HCF = x, LCM = 26x
And x + 26x = 729
⇒ 27x = 729 ⇒ x = 27
HCF = 27 and LCM = 702
Product of two numbers = HCF × LCM
⇒ 81 × 2nd number = 27 × 702
2nd number = (27 × 702) / 81 = 234

44. The HCF of two numbers is 29 and the other two factors of their LCM are 13 and 17. The smallest of the two numbers is: [RRB NTPC 09/02/2021 (Evening)]

Correct Answer: (c) 377 
Solution:

Smaller number = 13 × 29 = 377

45. The LCM of two co-prime numbers is 638. If one number is 29, then the other number is. [RRB NTPC 11/02/2021 (Morning)]

Correct Answer: (b) 22
Solution:

HCF of co-prime numbers = 1
Product of two numbers = LCM × HCF
⇒ 29 × 2nd number = 638 × 1
⇒ 2nd number = 638 / 29 = 22

46. Three whole cakes weigh 4½ lbs, 6¾ lbs and 7⅕ lbs, respectively. Each cake has to be divided into pieces of equal weight. Each piece must be as heavy as possible. If one such piece is served to each guest, then what are the maximum number of guests that can be served? [RRB NTPC 11/02/2021 (Morning)]

Correct Answer: (d) 41
Solution:

47. What is the greatest number that will divide 38, 45, 52 and leave as remainders 2, 3, and 4 respectively? [RRB NTPC 11/02/2021 (Evening)]

Correct Answer: (a) 6 
Solution:

The remainders are = 2, 3, 4
38 − 2 = 36
45 − 3 = 42
52 − 4 = 48
HCF of (36, 42, 48) = 6

48. The LCM of 248 and 868 is 1736. What is the HCF?

Correct Answer: (d) 124
Solution:

Given, 1st number = 248,
2nd number = 868, LCM = 1736
The product of two number = HCF × LCM
248 × 868 = HCF × 1736
HCF = 124