HCF and LCM – Railway Maths Part II

Total Questions: 50

21. Which of the following pairs of numbers is co-prime? [Group D 25/08/2022 (Afternoon)]

Correct Answer: (a) (17, 23)
Solution:

Co-prime numbers are those whose H.C.F is 1
By options, H.C.F of (17, 23) = 1

22. The LCM of two numbers is 385 and their HCF is 7. If the sum of the two numbers is 112, then their difference is: [Group D 25/08/2022 (Evening)]

Correct Answer: (c) 42
Solution:

Let the numbers are a and b
Product of the numbers (ab) = L.C.M × H.C.F = 385 × 7 = 2695
Sum of the numbers (a + b) = 112
Difference of the numbers

23. Find the greatest number by which when the numbers 57, 95 and 211 are divided, it leaves the same remainder in each case. [Group D 26/08/2022 (Morning)]

Correct Answer: (d) 2
Solution:

For same remainder, we have to find the HCF of the difference between the given numbers.
95 − 57 = 38 , 211 − 95 = 116 , 211 − 57 = 154
HCF of 38, 116 and 154 = 2
Therefore option (d) will be the right answer.

24. If the sum of two numbers is 54 and the LCM and HCF of these numbers are 84 and 6, respectively, then the sum of the reciprocal of the numbers is: [Group D 29/08/2022 (Afternoon)]

Correct Answer: (b) 3/28
Solution:

Sum of the numbers (x + y) = 54,
L.C.M = 84 , H.C.F = 6
Sum of their reciprocals

25. Two numbers are in the ratio 3 : 2. Their LCM and HCF are 24 and 4, respectively. The greater of the two numbers is: [Group D 29/08/2022 (Evening)]

Correct Answer: (b) 12
Solution:

Let the numbers be 3x and 2x
Product of the numbers = L.C.M × H.C.F = 24 × 4 = 96
3x × 2x = 96 ⇒ 6x² = 96 ⇒ x = √(96/6) = 4
Greater number = 3x = 12

26. If X is the greatest number that can divide 3808, 4798 and 5128 leaving the same remainder 13, then the sum of digits in X is: [Group D 30/08/2022 (Morning)]

Correct Answer: (b) 12 
Solution:

3808 − 13 = 3795 ,
4798 − 13 = 4785 ,
5128 − 13 = 5115
H.C.F of 3795, 4785 and 5115 = 165
Sum of the digits = 1 + 6 + 5 = 12

27. The LCM and HCF of two numbers are 1920 and 4, respectively. If one of the numbers is 60 then the other number is ______. [Group D 30/08/2022 (Afternoon)]

Correct Answer: (d) 128
Solution:

28. If the HCF and LCM of two numbers are 7 and 245, respectively, then their product is: [Group D 30/08/2022 (Evening)]

Correct Answer: (b) 1715 
Solution:

Product of two numbers = L.C.M × H.C.F = 245 × 7 = 1715

29. The product of the LCM and HCF of two numbers is 48. If the two numbers differ by 13, then find the numbers. [Group D 01/09/2022 (Morning)]

Correct Answer: (a) 3 and 16
Solution:

Let the numbers be x and y.
xy = 48 , x − y = 13  …(1)
x + y = √((x − y)² + 4xy) = √(169 + 192) = √361 = 19  …(2)
By solving eq. (1) and (2) we get,
x = 16 and y = 3
Hence the numbers are 3 and 16.

30. Three numbers are in the ratio 1 : 2 : 5 and their LCM is 1600. Find the HCF of the numbers. [Group D 01/09/2022 (Afternoon)]

Correct Answer: (c) 160 
Solution: