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Let x be the least number between 1400 and 1800, which when divided by 5, 6, 8, 9 and 12, the remainder in each case is 3. When x is divided by 11, the remainder is∶ 
1. 2
2. 1
3. 5
4. 3

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Correct Answer - Option 1 : 2

Given:

x be the least number between 1400 and 1800

Concept used:

Required number = (LCM of 5, 6, 8, 9 and 12) + 3

Calculation:

Factor of 5 = 1 × 5

⇒ Factor of 6 = 2 × 3

⇒ Factor of 8 = 2 × 2 × 2 

⇒ Factor of 9 = 3 × 3

⇒ Factor of 12 = 2 × 2 × 3

⇒ LCM of 5, 6, 8, 9 and 12 = 2 × 2 × 2 × 3 × 3 × 5 = 360

x be the least number between 1400 and 1800 so,

number x = 360 × 4 + 3 = 1443

When number x is divided by 11 remainder is = 1443/11 = 2

∴ number x is divided by 11 remainder is 2.

 

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