HCF and LCM – (Railway Maths Part VIII)

Total Questions: 27

11. Find the LCM of 48 and 54? [ALP Tier II 21/01/2019 (Afternoon) ]

Correct Answer: (c) 432
Solution:

48 = 2 × 8 × 3
54 = 2 × 9 × 3
L.C.M. (48,54) = 2 × 3 × 8 × 9 = 432

12. The least number consisting of five digits which is divisible by 97 is x. What is the sum of the digits of X?

Correct Answer: (c) 17
Solution:

Smallest 5 digit number = 10000 Dividing 10000 by 97, we get the remainder as 9. The smallest 5 digit number
= (10000 + 97 − 9) = 10088.
So, sum of the digits of the number
= 1 + 0 + 0 + 8 + 8 = 17

13. The LCM of two numbers is 48. Their ratio is 2 : 3. Find the sum of the numbers? [ALP Tier II 21/01/2019 (Morning) ]

Correct Answer: (d) 40
Solution:

Let, the numbers are 2x and 3x. LCM (2x, 3x) = 2 × 3 × x
According to question,
2 × 3 × x = 48 ⇒ x = 8
Then, sum of numbers
(2x + 3x) = 5x = 40

14. Find the least common multiple of 56 and 50. [ALP Tier II 23/01/2019 (Afternoon) ]

Correct Answer: (c) 1400
Solution:

L.C.M. of (56, 50) = 1400

15. LCM of two numbers 64 and HCF is 16 .If one of them is 64, find the second number. [RPF Constable 17/01/2019 (Evening) ]

Correct Answer: (b) 16
Solution:

L.C.M. × H.C.F. = 1st number × 2nd number
64 × 16 = 64 × X ⇒ X = 16

16. LCM of two numbers is 156 and their HCF is 12. Given that one number is 12, find the second number. [RPF Constable 18/01/2019 (Morning) ]

Correct Answer: (c) 156
Solution:

L.C.M. × H.C.F. = 1st number × 2nd number
156 × 12 = 12 × X ⇒ X = 156

17. The least common multiple of two numbers is 182 and their highest common factor is 13. If one of the number 13, then find the second number?

Correct Answer: (a) 182
Solution:

L.C.M. × H.C.F. = 1st number × 2nd number
182 × 13 = 13 × x ⇒ x = 182

18. Find the product of numbers whose LCM is 30 and HCF is 9. [RPF S.I. 19/12/2018 (Morning) ]

Correct Answer: (d) 270
Solution:

As we know that product of L.C.M. and H.C.F. of the numbers is equal to products of the numbers, L.C.M. × H.C.F. = 1st number × 2nd
number
1st number × 2nd number = 30 × 9 = 270

19. Find the product of two numbers whose least common factor (LCM) is 45 and greatest common factor (HCF) is 10. [RPF S.I. 19/12/2018 (Evening) ]

Correct Answer: (a) 450
Solution:

As we know that product of L.C.M. and H.C.F. of the numbers is equal to products of the numbers, L.C.M. × H.C.F. = 1st number × 2nd
number
1st number × 2nd number = 45 × 10 = 450

20. Tapas, Avi and Rishi shared a cake. Tapas had 1/2 of it, Rishi had 1/3 of it and Avi had the rest. What was Avi's share of the cake? [RRB ALP 09/08/2018 (Morning) ]

Correct Answer: (b) 1/6
Solution:

Let the total no of cakes be 6
i.e. LCM of (2,3)
No of cakes that Tapas had = 1/2 × 6 = 3
No of cakes that Rishi had = 1/3 × 6 = 2
Remaining cakes = 6 − (3 + 2) = 1
Avi’s share of the cake = 1/6