HCF and LCM – Railway Maths Part IV

Total Questions: 50

41. Find three numbers such that their ratio is 3 : 4 : 5 and their HCF is 7. [RRB NTPC 16/01/2021 (Morning)]

Correct Answer: (c) 21; 28; 35
Solution:

1st Number = 3 × 7 = 21
2nd Number = 4 × 7 = 28
3rd Number = 5 × 7 = 35

42. Determine the smallest number which when divided by 12, 16, 20, 25 and 30 leaves the same remainder 3 in each case. [RRB NTPC 16/01/2021 (Morning)]

Correct Answer: (b) 1203
Solution:

LCM of (12, 16, 20, 25, 30) = 1200
The Required smallest number = 1200 + 3 = 1203

43. What will be the smallest number which on adding 25 to it, is exactly divisible by 25, 36 and 40? [RRB NTPC 16/01/2021 (Evening)]

Correct Answer: (d) 3575
Solution:

LCM of (25, 36, 40) = 1800
Number should be multiple of 1800
1800 × 2 = 3600
Required smallest number = 3600 - 25 = 3575

44. Find the least number which is divisible by first ten natural numbers. [RRB NTPC 17/01/2021 (Morning)]

Correct Answer: (c) 2520
Solution:

Divisible by the first ten natural numbers means that number should be divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
LCM of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 = 2520

45. The least number that should be added to 5474 so that the number is exactly divisible by 3, 4, 6 and 8 is: [RRB NTPC 18/01/2021 (Morning)]

Correct Answer: (c) 22
Solution:

Divisible by the first ten natural numbers means that number should be divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
LCM of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 = 2520

46. The L.C.M of two consecutive positive integers x and x+1 is: [RRB NTPC 18/01/2021 (Evening)]

Correct Answer: (b) x(x + 1)
Solution:

The L.C.M of any two consecutive positive integers x and x + 1 is always the multiple of those two numbers = x(x + 1);
Example - the L.C.M of 6, 7 = 42.

47. If LCM and HCF of two numbers are 70 and 7 respectively and if one number is 35, then what will be the second number? [RRB NTPC 18/01/2021 (Evening)]

Correct Answer: (d) 14
Solution:

As we know product of any two numbers = product of LCM and HCF of those two numbers;
Then the second number will be = (70 × 7) / 35 = 14

48. The LCM of two numbers is the 20th multiple of 3. If their HCF is 6 and one of the number is 12, then the second one is. [RRB NTPC 19/01/2021 (Morning)]

Correct Answer: (c) 30
Solution:

LCM = 20 × 3 = 60, HCF = 6
First Number = 12
Second Number = (LCM × HCF) ÷ First Number
Second Number = (60 × 6) ÷ 12 = 30

49. The HCF and LCM of two number are 6 and 36 respectively. If one of the number is 12, then the other number is: [RRB NTPC 19/01/2021 (Morning)]

Correct Answer: (b) 18
Solution:

Second Number = (HCF × LCM) ÷ First number
Second Number = (6 × 36) ÷ 12
Second Number = 18

50. A physical education teacher has to distribute 96 bats and 180 balls among a number of player, such that all players get the same number of bats and likewise, all players get the same number of balls. what will be the greatest number of players receiving the gift? [RRB NTPC 20/01/2021 (Morning)]

Correct Answer: (b) 12
Solution:

The highest number of players receiving the gifts will be
= the HCF of 96, 180 = 12 ;