HCF and LCM – Railway Maths Part Ⅴ

Total Questions: 48

1. Q.203. The HCF of 24 and 144 is ‘10p + 4’, then the value of p is: [RRB NTPC 20/01/2021 (Evening)]

Correct Answer: (c) 2
Solution:

H.C.F. of 24 and 144 = 24
A/Q, 10p + 4 = 24
⇒ 10p = 20 ⇒ p = 2

2. The LCM of two numbers is 721, and the numbers are in the ratio of 1 : 7. What is the sum of the numbers? [RRB NTPC 21/01/2021 (Morning)]

Correct Answer: (a) 824
Solution:

Let the numbers be x and 7x.
LCM of x and 7x = 7x
A/Q, 7x = 721 ⇒ x = 103
Sum of both numbers
= 8x = 8 × 103 = 824

3. What is the LCM of ²√169 , ∛27, ∛64 and ²√144 [RRB NTPC 21/01/2021 (Morning)]

Correct Answer: (b) 156
Solution:

²√169 = 13, ³√27 = 3, ³√64 = 4, ²√144 = 12
LCM of (13, 3, 4, 12) = 156

4. LCM of two numbers is 78. Their GCD is 13. If one of the numbers is 26, then the other number is... [RRB NTPC 21/01/2021 (Evening)]

Correct Answer: (a) 39
Solution:

Given, LCM = 78, HCF/GCD = 13 and one number = 26
Let, the 2nd number = X
We know that, the product of the two numbers = LCM × HCF
26 × X = 78 × 13 ⇒ X = 39

5. If the HCF of 85 and 153 is expressible in the form of 85x - 153, then the value of x is: [RRB NTPC 21/01/2021 (Morning)]

Correct Answer: (d) 2
Solution:

HCF of 85 and 153 = 17
Then 17 = 85x – 153
x = 170 ÷ 85 = 2

6. The LCM of 63, 36 and x is 252. Which of the following options can not be the value of x? [RRB NTPC 22/01/2021 (Evening)]

Correct Answer: (d) 56
Solution:

252 is divisible by 63, 36, 28, 42, 14 but 252 is not divisible by 56.
So, x ≠ 56

7. Find the smallest number that is exactly divisible by 7, 14, 28, 35 and 42. [RRB NTPC 23/01/2021 (Morning)]

Correct Answer: (d) 420
Solution:

LCM of (7, 14, 28, 35, 42) = 420

8. Two numbers are in the ratio of 2 : 3 and the product of their LCM and HCF is 9600. The sum of the number is: [RRB NTPC 23/01/2021 (Morning)]

Correct Answer: (c) 200
Solution:

Let the numbers be 2x and 3x
HCF × LCM = Product of two numbers
⇒ 9600 = 2x × 3x ⇒ 9600 = 6x²
⇒ x² = 1600 ⇒ x = 40
Sum of numbers = 5x = 5 × 40 = 200

9. The product of two co-prime numbers is 119. Their LCM should be: [RRB NTPC 23/01/2021 (Morning)]

Correct Answer: (a) 119
Solution:

Co-prime numbers are the pair of numbers having HCF = 1
LCM of co-prime numbers = product of numbers = 119

10. What is the greatest number that will divide 2400 and 1810 and leave remainders 6 and 4 respectively? [RRB NTPC 25/01/2021 (Morning)]

Correct Answer: (a) 42 
Solution:

Subtracting 6 from 2400 and 4 from 1810
2400 – 6 = 2394, 1810 – 4 = 1806
HCF of 2394 and 1806 is
2394 → 2 × 3 × 3 × 7 × 19
1809 → 2 × 3 × 7 × 43
HCF (2394, 1806) = 42
42 is the greatest number that will divide 2400 and 1810 and leave remainder 6 and 4.