HCF and LCM – Railway Maths

Total Questions: 50

41. Find the HCF of (3⁴⁵ − 1) and (3³⁵ − 1). [NTPC CBT - I 17/01/2021 (Morning)]

Correct Answer: (d) 242
Solution:

Numbers are (3⁴⁵ − 1) and (3³⁵ − 1)
HCF of 45 and 35 = 5
HCF of (3⁴⁵ − 1) and (3³⁵ − 1) = 3⁵ − 1 = 243 − 1 = 242

42. What is the product of LCM and HCF of 18 and 42? [NTPC CBT - I 18/01/2021 (Evening)]

Correct Answer: (c) 756
Solution:

As we know product of any two numbers = product of LCM and HCF of those two numbers;
So, the product of LCM and HCF of 18 and 42 = 18 × 42 = 756

43. f the HCF of 51 and 85 is expressed in the form of 51m - 85, then the value of m will be: [NTPC CBT - I 20/01/2021 (Morning)]

Correct Answer: (d) 2
Solution:

The HCF of 51 and 85 is = 17;
So, 51m − 85 = 17
51m = 17 + 85 ⇒ m = 2

44. If P = a × m × r and Q = b × m × 2 × r, where a, b, m, r are odd primes. Then the HCF of P and Q is.. [NTPC CBT - I 21/01/2021 (Evening)]

Correct Answer: (d) m r
Solution:

ATQ,
P = a × m × r
Q = b × m × 2 × r (where a, b, m, r are odd primes)
Since HCF is common factor presence in all terms,
So HCF of P and Q will be mr.

45. A number lies between the cubes of 11 and 12. If the number is divisible by twice of 80 and 6 both, what will the number? [NTPC CBT - I 29/01/2021 (Morning)]

Correct Answer: (d) 1440
Solution:

The number is divisible by 160 and 12 both.
So the number must be divisible by LCM of 160 and 12.
LCM of 160 and 12 = 480
The required number should be multiple of 480.
480 × 3 = 1440

46. The LCM of two positive integers is thrice the larger number. The difference of the smaller number and the HCF of two numbers is 6. The smaller number is: [NTPC CBT - I 31/01/2021 (Evening)]

Correct Answer: (a) 9
Solution:

Let the smaller number = a
And bigger number = b
A/Q, LCM = 3b
And a − HCF = 6 ⇒ HCF = a − 6
HCF × LCM = Product of two numbers
⇒ (a − 6) × 3b = ab
⇒ 3a − 18 = a ⇒ 2a = 18 ⇒ a = 9

47. If a, b, c, d are four numbers, such that the LCM of a and b is b, the LCM of b and c is c and the LCM of c and d is d, then the LCM of a, b, c, and d will be: [NTPC CBT - I 03/02/2021 (Morning)]

Correct Answer: (a) d
Solution:

LCM of a and b = b
LCM of b and c = c
LCM of a, b, c = c
LCM of c and d = d
So, LCM of a, b, c, and d = d

48. The HCF of two numbers is 19 and the other two factors of their LCM are 11 and 13. The larger of the two numbers is: [NTPC CBT - I 04/02/2021 (Evening)]

Correct Answer: (c) 247
Solution:

Two factors of their LCM are 11 and 13
So the numbers will be
11 × HCF and 13 × HCF
Larger number = 13 × 19 = 247

49. If the sum of two numbers is 84 and their HCF and LCM are 3 and 124 respectively, the sum of the reciprocals of the two numbers will be: [NTPC CBT - I 04/02/2021 (Evening)]

Correct Answer: (d) 7/31
Solution:

Let the numbers be x and y
A/Q, x + y = 84
Product of two numbers = HCF × LCM
⇒ xy = 3 × 124 = 372
Now,
1/x + 1/y = (x + y) / xy = 84 / 372 = 7 / 31

50. Three different containers contain a mixture of milk and water, measuring 403 litres, 434 litres and 465 litres, respectively. The biggest measure required to measure all the different quantities exactly is: [NTPC CBT - I 11/02/2021 (Morning)]

Correct Answer: (c) 31 litres
Solution:

HCF of (403, 434, 465) = 31
The biggest measure required to measure all the different quantities exactly is = 31 litres