Which is the least number of $5$ digits exactly divisible by each of $3, 4, 5, 6, 7$ and $8 ?$

9240

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10080

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9996

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100000

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Solution

The correct option is A $10080$
Least number of 5 digits $= 10000.$
L.C.M of $3, 4, 5, 6, 7, 8 = 840.$
Dividing $10000$ by $840$ we get the remainder
as $760.$
$∴$ Required number
$= 10000 + (840 - 760)$
$= 10000 + 80 = 10080$

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