HCF and LCM – Railway Maths Part III

Total Questions: 52

51. Let x be the least four-digit number which when divided by 18, 27, 30, 40 and 45, the remainder in each case is 9. Find the remainder when x is divided by 37. [Level 3 (14/06/2022) Shift 2]

Correct Answer: (a) 16
Solution:

Least four-digits number = 1000
LCM of 18, 27, 30, 40, and 45 = 1080
Remainder in each case = 9
So, number = 1080 + 9 = 1089
When 1089 is divided by 37,
remainder = 16

52. The HCF of two numbers is 8 and the product of the two numbers is 6400. How many pairs of numbers exist, which satisfy the above conditions? [Level 3 (14/06/2022) Shift 2]

Correct Answer: (b) 2
Solution:

According to the question,
8P × 8Q = 6400 ⇒ PQ = 100
Number of possible pairs = (4, 25) and (1, 100)