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Q.

Determine the number nearest to 110000 but greater than 100000 which is exactly divisible by each of 8, 15 and 21 .


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a

109201

b

109200

c

109202

d

109203 

answer is B.

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Detailed Solution

Given to find the number nearest to 110000 but greater than 100000 which is exactly
divisible by each of 8, 15 and 21.
LCM is the smallest number that is divisible by all of the numbers whose LCM is being calculated.
Calculate LCM of 8, 15 and 21.
   geogebra-export (24) LCM=2×2×2×3×5×7 LCM=840   Therefore, LCM of 8, 15 and 21 is 840.
 Thus, the number nearest to 110000 but greater than 100000 which is exactly divisible by 8, 15 and 21
Divide 110000 by 840 using Long Division method,
  geogebra-export (25)Quotient obtained is 130 and remainder is 800.
∴  number nearest to 110000 but greater than 100000 which is exactly divisible by 8, 15 and 21 = 110000−800  
⇒  109200
Therefore, number nearest to 110000 but greater than 100000 which is exactly divisible by 8, 15 and 21 is 109200.
Hence the correct option is 2.
 
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Determine the number nearest to 110000 but greater than 100000 which is exactly divisible by each of 8, 15 and 21 .