Question 894550
{{{2*3*4*5*6*7=19320}}}


Factor 4 includes 2 already.
Factor 6 includes 2 and 3 already.


{{{2*3*(2*2)*5*(2*3)*7=19320}}}


Eliminate one of 3.
{{{2*3*(2*2)*5*(2)*7=6440}}}, seems a little too less.
Put back the 3.
{{{2*3*(2*2)*5*(2*3)*7=19320}}}


Eliminate one of 2.
{{{2*3*(2)*5*(2*3)*7=9960}}}-----This should be one of the numbers.


Can you find a way to reach a number greater than 10000 but not more than 19320?
19320 is farther from 10000 than 6440 is from 10000; based on this,  the other number you want should be 6440.


The two numbers nearest to 10000 exactly divisible by 2,3,4,5,6,7 are <b>6440 and 9960</b>.