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It is given that the set of numbers are \[2,3,4,6,8,9,11\]

We have to find the seven digit number is divisible by each of \[2,3,4,6,8,9,11\]

First we find the least common multiple for the set of given numbers.

Here \[{2^3} \times 9 \times 11 = 792\] is the least common multiple for the set of given numbers.

First we take the least seven digit number \[10,00,000\] is divisible by \[792\]

Then, we get quotient \[ = 1262\] and remainder \[ = 496\]

Here, we are trying to find the least seven digit number which is divisible by \[792\]

\[\therefore 792 \times 1262 = 999504\] but it is greatest six digit number which divisible by \[792\]

Also \[10,00,000\] is not perfectly divide by \[792\] , where \[792 \times 1262 = 999504\] is greatest six digit number if we add by \[792\] , it is the first seven digit number divisible by \[792\] .

Add \[999504 + 792 = 1000296\] it is the least seven digit number which is divisible by \[792\],

Suppose we take a greatest seven digit number \[99,99,999\] divisible by \[792\]

Then we get, quotient=\[12626\], remainder \[ = 207\]

Also \[99,99,999\] is not perfectly dividing by \[792\], so either we can subtract \[99,99,999\] by \[207\] or multiply \[12626\] by\[792\].

Therefore, \[792 \times 12626 = 9999792\] it is the greatest seven digit number which is divisible by \[792\]

Hence the set of seven digit number which is divisible by \[792 = \{ 1000296,1001088,....9999792\} \]

From the set the number we obtained \[792 \times 1307 = 1035144\] .