HCF and LCM – Railway Maths Part II

Total Questions: 50

31. If the product of two numbers, not necessarily distinct from each other, is 25 and their HCF is 5, then their LCM is: [Group D 01/09/2022 (Evening)]

Correct Answer: (d) 5
Solution:

32. If the ratio of two numbers is 4 : 3 and the product of their LCM and their HCF is 432, then the sum of the reciprocals of the LCM and the HCF is: [Group D 01/09/2022 (Evening)]

Correct Answer: (a) 13/72 
Solution:

Let the numbers are 4x and 3x.
4x × 3x = 432 ⇒ 12x² = 432 ⇒ x = √36 = 6
Numbers are 24, 18
L.C.M = 72 and H.C.F = 6

33. The sum of two numbers is 35 and their LCM is 306. The two numbers are: [Group D 02/09/2022 (Morning)]

Correct Answer: (c) 17, 18
Solution:

Let the numbers be x and y.
x + y = 35 and L.C.M of x and y = 306
306 = 2 × 3 × 3 × 17 = 18 × 17
H.C.F = 1; first number = 17 and second number = 18

34. Four bells ring at intervals of 4 minutes, 8 minutes, 12 minutes, and 24 minutes respectively. All the four bells rang together at 12 noon. How many times after 12 noon will the four bells ring together in the next four hours, with the ringing at 4 p.m. being included? [Group D 02/09/2022 (Afternoon)]

Correct Answer: (a) 10 times
Solution:

L.C.M of 4, 8, 12, and 24 = 24 minutes
After every 24 minutes four bells will ring together.
Now, no. of times they will ring in 4 hrs = (4 × 60)/24 = 10 times

35. If the product of two numbers is 8410 and their HCF is 29, then their LCM is: [Group D 05/09/2022 (Morning)]

Correct Answer: (b) 290 
Solution:

L.C.M × H.C.F = Product of two number

36. The smallest four-digit number that is exactly divisible by each of 24, 40 and 56 is: [Group D 05/09/2022 (Afternoon)]

Correct Answer: (b) 1680
Solution:

Smallest 4-digit number = 1000
From factorization,
24 = 2³ × 3
40 = 2³ × 5
56 = 2³ × 7
L.C.M of 24, 40 and 56 = 840
Now, 840 × 2 = 1680
Hence, the required number which is completely divisible by each of 24, 40 and 56 = 1680

37. Let x be the greatest number which on dividing 7072, 8505 and 9925 leaves remainders 22, 45 and 55 respectively. Find the sum of the digits of x. [Group D 06/09/2022 (Morning)]

Correct Answer: (a) 6 
Solution:

38. A conference is being organized by an educational institution, where the participants will be teachers of different subjects. The number of participants in Physics, Chemistry and Mathematics are 112, 144 and 192 respectively. Equal number of participants are to be seated in each room, and all the participants sitting in a room should be teachers of the same subject. Find the minimum number of rooms required for the event. [Group D 06/09/2022 (Afternoon)]

Correct Answer: (d) 28
Solution:

39. In finding the Highest common factor (HCF) of two numbers by division method, the quotients are 1, 5 and 2 respectively, and the last divisor is 15. Find the least common multiple (LCM) of those two numbers. [Group D 06/09/2022 (Evening)]

Correct Answer: (d) 2145
Solution:

As we know,
Dividend = Divisor × Quotient + Remainder
Last divisor = 15 and quotient = 2
Dividend = 15 × 2 = 30
Now,
Divisor = 30, Quotient = 5, Remainder = 15
Dividend (a) = 30 × 5 + 15 = 165
Again,
Divisor = 165, Quotient = 1, Remainder = 30
Dividend (b) = 165 × 1 + 30 = 195
Hence two numbers = a = 165, b = 195
Least common multiple = 2145

40. When 1833, 2482 and 3190 are divided by the greatest number x, the remainder in each case is y. What is the value of (3x − 14y)? [Group D 08/09/2022 (Afternoon)]

Correct Answer: (c) 121 
Solution: