HCF and LCM – (Railway Maths Part VII)

Total Questions: 50

31. Find the LCM of two numbers, if their HCF is 2 and product is 120. [RRB NTPC 26/07/2021 (Evening) ]

Correct Answer: (d) 60
Solution:

32. The LCM of two numbers is 1024, and one of them is a prime number. Find their GCD. [RRB NTPC 31/07/2021 (Morning) ]

Correct Answer: (c) 2
Solution:

33. What is the least number that when divided by 18 and 24 leaves a remainder of 11 and 17, respectively? [RRB NTPC 31/07/2021 (Morning) ]

Correct Answer: (b) 65
Solution:

18 - 11 = 7, 24 - 17 = 7
Required number = LCM of (24,18) - 7
= 72 - 7 = 65

34. Find the least number which when divided by 20,25,35 and 40 leaves remainders 15,20,30 and 35 respectively. [RRB NTPC 31/07/2021 (Evening) ]

Correct Answer: (c) 1395
Solution:

LCM of (20, 25, 35, 40) = 1400
20 - 15 = 25 - 20 = 35 - 30 = 40 - 35 = 5
Required least number = 1400 - 5 = 1395

35. What are the LCM and HCF of the reciprocals of 18 and 24? [RRB JE 22/05/2019 (Afternoon) ]

Correct Answer: (d) 1/6, 1/72
Solution:

36. Product of two coprime numbers is 903. Find their LCM. [RRB JE 22/05/2019 (Afternoon) ]

Correct Answer: (d) 903
Solution:

Product of two co-prime number = 903 As we know, the product of two co-prime numbers is equal to their L.C.M.
So, L.C.M of the two numbers = 903

37. The LCM of two numbers which are in the ratio 2 : 3 is 48. What is their sum? [RRB JE 22/05/2019 (Evening) ]

Correct Answer: (d) 40
Solution:

Let the H.C.F of both the number = x
Numbers are in the ratio 2x and 3x
⇒ 6x = 48 ⇒ x = 8
Required sum → 16 + 24 = 40

38. Two numbers are in the ratio 4 : 5. Their LCM is 180. What is their sum? [RRB JE 24/05/2019 (Evening) ]

Correct Answer: (a) 81
Solution:

Let number be 4x and 5x So LCM of 4x and 5x is 20x
According to the question,
20x = 180 ⇒ x = 9
So numbers will be 4x ⇒ 4 × 9 = 36
And 5x ⇒ 5 × 9 = 45
So the sum is 36 + 45 = 81

39. Find the least number which when divided by 5, 6, 7, 8, leaves a remainder 3, and is also a multiple of 9. [RRB JE 26/05/2019 (Afternoon) ]

Correct Answer: (c) 1683
Solution:

40. There are three cans of milk containing 36 litres, 45 litres and 72 litres. Find the biggest measure that can measure all these exactly. [RRB JE 28/05/2019 (Morning) ]

Correct Answer: (c) 9 litres
Solution:

HCF of (36 , 45 , 72) = 9
The biggest measurment that can measure all these exactly = 9