What is the least number which, when divided by 5, 6, 8 and 10 leaves a remainder of 2 in each case?

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RRB ALP Electrician 22 Jan 2019 Official Paper (Shift 2)
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  1. 128
  2. 122
  3. 162
  4. 118

Answer (Detailed Solution Below)

Option 2 : 122
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Detailed Solution

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Given:

The least number which when divided by 5, 6, 8, and 10 leaves a reminder 2.

Concept used:

For the least number take LCM, also have to check that all conditions are satisfying or not.

For the same remainder in each case add the remainder with the LCM.

Calculation:

LCM of 5, 6, 8, 10

5 = 5 × 1

6 = 2 × 3 × 1

8 = 2 × 2 × 2

10 = 2 × 5

LCM = 2 × 2 × 2 × 3 × 5 = 120

For same remainder, we have to add 2 to LCM = (120 + 2) = 122

∴ The answer is 122.

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