1.

When 20, 24, 32, and 40 divided the least number x, the remainder in each case is 9 but x is divisible by 9. What is the unit digit in x?1. 82. 43. 54. 9

Answer» Correct Answer - Option 4 : 9

Concept:

The LCM of two or more given numbers is the least number which is exactly divisible by each of them.

Caclculation:

2

20, 24, 32, 40

2

10, 12, 16, 20

2

5, 6, 8, 10

2

 5, 3, 4, 5

2

 5, 3, 2, 5

3

 5, 3, 1, 5

5

 5, 1, 1, 5

 

 1, 1, 1, 1

L.C.M. = 2 × 2 × 2 × 2 × 2 × 3 × 5 = 480

Given, x should be divisible by 9.

Let (480k + 9) is divisible by 9.

x = (480k + 9)

Put k = 1, 2, 3, 4, 5…..

(i) When, k = 1, x = 489 is not divisible by 9.

(ii) When, k = 2, x = 969 is not divisible by 9.

(iii) When, k = 3, x = 1449 is divisible by 9.

⇒ x = 1449

∴ The unit digit of x is 9.


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