HCF and LCM – (Railway Maths Part VII)

Total Questions: 50

41. Find the maximum number of children among whom 429 pencils and 715 pens can be equally distributed. [RRB JE 28/05/2019 (Afternoon) ]

Correct Answer: (d) 143
Solution:

The maximum number of children = HCF of (429,715) =143

42. If A, B are two natural numbers >1 and their H.C.F is 1, then which of these statements is always TRUE? [RRB JE 31/05/2019 (Evening) ]

Correct Answer: (a) A, B are coprime to each other
Solution:

Because we know that HCF of co- prime number is always 1

43. Two numbers are in the ratio 1 : 4 and their LCM and HCF are 84 and 21. Find the smaller number. [RRB JE 01/06/2019 (Morning) ]

Correct Answer: (b) 21
Solution:

Let, the first number 𝑥 and second number 4 𝑥
first number × second number
= L.C.M × H.C.F
(x) × (4x) = 84 × 21 → x = 21
So , the smallest number is 21.

44. Find the Greatest number that will exactly divide 25, 35, 40,and 30. [RRB JE 01/06/2019 (Afternoon) ]

Correct Answer: (d) 5
Solution:

Greatest number that will exactly divide 25, 35, 40,and 30
⇒ HCF of (25, 35, 40, and 30) ⇒ 5

45. The sum of LCM and HCF of two numbers is 372. If LCM is equal to 92 times of HCF and one of the numbers is 368, what is the other number? [RRB JE 01/06/2019 (Evening) ]

Correct Answer: (a) 4
Solution:

46. A father is aged twice more than his son. The HCF of their ages is 22. What is the son's age? [RRB JE 02/06/2019 (Morning) ]

Correct Answer: (c) 22 years
Solution:

Let the age of father and son be 2x years and x years.
According to question, HCF(2x , x) = x = 22 So,the age of son is 22 years.

47. Find the least multiple of 7 that leaves the remainder 4 when divided by 6, 9, 15 and 18. [RRB JE 02/06/2019 (Morning) ]

Correct Answer: (d) 364
Solution:

48. Two numbers in the ratio 15 : 11 have their HCF to be 13. What is their LCM? [RRB JE 02/06/2019 (Evening) ]

Correct Answer: (a) 2145
Solution:

49. The sum of two numbers is 232. Their HCF is 29. Which of these pairs give the possible values of the numbers? [RRB JE 02/06/2019 (Evening) ]

Correct Answer: (b) 29, 203
Solution:

50. Find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively. [RRB JE 26/06/2019 (Morning) ]

Correct Answer: (d) 127
Solution: