HCF and LCM – Railway Maths Part II

Total Questions: 50

41. The HCF and LCM of two numbers are 24 and 456, respectively. If one number is 96, then the other number is: [Group D 08/09/2022 (Evening)]

Correct Answer: (c) 114 
Solution:

1st no. × 2nd no. = L.C.M × H.C.F
Other number = (L.C.M × H.C.F) / first number = (24 × 456)/96 = 114

42. The least 3-digit number that is completely divisible by 8 and 12 is: [Group D 12/09/2022 (Morning)]

Correct Answer: (a) 120
Solution:

The least number will be LCM of 8 and 12
So LCM of 8 and 12 = 24
Required value = 24 × 5 = 120

43. The greatest number which divides 72 and 122 leaving remainders 3 and 7, respectively, is: [Group D 12/09/2022 (Afternoon)]

Correct Answer: (c) 23
Solution:

After subtracting remainder number be

72122
−3  -3
69115


HCF of 69 and 115 will be the required number,
HCF of 69 and 115 = 23

44. If the ratio of two numbers is 5 : 7, and HCF is 8, then their LCM is: [Group D 13/09/2022 (Morning)]

Correct Answer: (c) 280
Solution:

Let the numbers be 5x and 7x.
H.C.F = 8
Then numbers = 40 and 56
Now, required L.C.M = 280

45. The LCM and the HCF of two numbers are given as 459 and 3, respectively. If one number is 51, then find the other number. [Group D 13/09/2022 (Morning)]

Correct Answer: (c) 27
Solution:

Other number = (L.C.M × H.C.F)/first number
= (459 × 3)/51 = 27

46. The HCF and the LCM of two numbers are 1080 and 30240, respectively. If one of the numbers is 4320, then the other number is: [Group D 13/09/2022 (Afternoon)]

Correct Answer: (d) 7560
Solution:

Other number = (L.C.M × H.C.F)/first number
= (1080 × 30240) / 4320 = 7560

47. Two numbers are in the ratio 11 : 17 and the difference between the numbers is 18. The HCF and the LCM of these numbers, respectively, are: [Group D 14/09/2022 (Afternoon)]

Correct Answer: (c) 3 and 561
Solution:

Let the numbers are 11x and 17x
17x − 11x = 18 ⇒ 6x = 18 ⇒ x = 3
Numbers = 33 and 51
Now, H.C.F of the numbers = 3
L.C.M of the numbers = 561

48. The LCM of two numbers is 1260 and their HCF is 30. If one of the two numbers is 180, find the other number. [Group D 14/09/2022 (Afternoon)]

Correct Answer: (d) 210
Solution:

49. Three numbers are in the ratio 5 : 6 : 8 and their LCM is 1200. The sum of the numbers is: [Group D 14/09/2022 (Evening)]

Correct Answer: (d) 190
Solution:

Let the numbers are 5x, 6x and 8x.
120x = 1200 ⇒ x = 10
Sum of the numbers = 5x + 6x + 8x
= 50 + 60 + 80 = 190

50. The HCF and the LCM of two number are 44 and 264, respectively. if one of the numbers is 3/2 times of the other, what is the smaller number? [Group D 16/09/2022 (Morning)]

Correct Answer: (c) 88
Solution: