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The greatest number of four digits which is divisible by each one of the numbers $12$, $18$, $21$ & $28$, is :

  1. $9848$
  2. $9864$
  3. $9828$
  4. $9636$
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The Answer is C

The greatest 4 digits number is 9999
The LCM of 12, 18, 21, 28 is 252
On dividing 9999 by 252 the remainder comes out to 171
Required number = 9999 - 171 = 9828

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Answer is C

Easiest way is to go with the options.

Set of numbers 12, 18, 21 and 28,

→ as 18 is there, we have to identify the options which are divisible by 9. For that, sum of the digits of the options given should be divisible by 9

→ Second criteria, as 21 and 28 are there, required number should be divisible by 7. Only option C is divisible by 7

The option which satisfies both the conditions is 9828

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