HCF and LCM – Railway Maths Part IV

Total Questions: 50

31. The LCM of two numbers is 91 times their HCF. The sum of the HCF and LCM is 2760. If one of the numbers is 210. Find the other number. [RRB NTPC 09/01/2021 (Morning)]

Correct Answer: (c) 390
Solution:

The LCM of two numbers is 91 times their HCF.
Let the HCF = x,
So the LCM = 91x,
According to the question,
91x + x = 92x = 2760
⇒ 92x = 2760 ⇒ x = 30
Again let the other number is y,
210 × y = 30 × 91 × 30
⇒ y = 390

32. The largest number which divides 55, 72 and 123 leaving the remainder 3, 7 and 6 respectively = ? [RRB NTPC 09/01/2021 (Evening)]

Correct Answer: (a) 13
Solution:

55 - 3 = 52, 72 - 7 = 65
123 - 6 = 117
The required number is the
HCF of (52, 65, 117) = 13

33. The least number that is divisible by all the numbers from 2 to 10 is [RRB NTPC 10/01/2021 (Morning)]

Correct Answer: (c) 2520
Solution:

All the numbers from 2 to 10 are: 2, 3, 4, 5, 6, 7, 8, 9, 10;
The LCM = 2520
Then the least number that is divisible by all the numbers from 2 to 10 is 2520.

34. Find the smallest number by which 720 should be multiplied, so that the product becomes a perfect square. [RRB NTPC 11/01/2021 (Morning)]

Correct Answer: (d) 5
Solution:

The prime factorisation of 720 = 2 × 2 × 2 × 2 × 3 × 3 × 5
Therefore one more 5 is needed for a complete square.

35. The LCM of two numbers is 24 times their HCF. The sum of the HCF and LCM is 750. If one of the numbers is 90, then find the other number. [RRB NTPC 11/01/2021 (Evening)]

Correct Answer: (a) 240
Solution:

Let the HCF = x, LCM = 24x
A/Q, x + 24x = 750
⇒ 25x = 750 ⇒ x = 30
∴ HCF = 30 And LCM = 720
HCF × LCM = Product of two numbers
⇒ 30 × 720 = 90 × 2nd number
⇒ 2nd number = (30 × 720) / 90 = 240

36. LCM and HCF of two numbers are 1920 and 16 respectively. If one of the numbers is 240, then the other number is: [RRB NTPC 12/01/2021 (Morning)]

Correct Answer: (a) 128
Solution:

LCM × HCF = Products of two numbers
⇒ 1920 × 16 = 240 × 2nd number
⇒ 2nd number = (1920 × 16) / 240 = 128

37. There are four table clocks. They ring every 10 min, 15 min, 20 min and 25 min respectively. If they all ring together at 10 a.m., Then at what time will they ring together again? [RRB NTPC 12/01/2021 (Evening)]

Correct Answer: (c) 3 : 00 p.m.
Solution:

LCM of 10, 15, 20, 25 = 300 min. = 5 hours
They ring together again at 10 a.m. + 5 = 3 p.m.

38. The greatest number of four digits which is divisible by 15, 20, 25 and 45 is. [RRB NTPC 13/01/2021 (Morning)]

Correct Answer: (c) 9900
Solution:

LCM of 15, 20, 25, 45 = 900
Greatest number of 4 digit = 9999
When we divide 9999 by 900 we get 99 as remainder.
The required 4 digit number = 9999 - 99 = 9900

39. The HCF and LCM of 36 and N are 9 and 180 respectively. N is equal to [RRB NTPC 13/01/2021 (Morning)]

Correct Answer: (c) 45
Solution:

HCF × LCM = 1st no. × 2nd no.
⇒ 9 × 180 = 36 × N ⇒ N = (9 × 180) / 36 = 45

40. Determine the LCM of [RRB NTPC 13/01/2021 (Evening)]

Correct Answer: (d) 40/3
Solution:

LCM of (2/3), (4/9), (8/15) and (10/21)
= (LCM of 2, 4, 8, 10) / (HCF of 3, 9, 15, 21) = 40 / 3