SOLUTION: determine the two numbers nearest to 10000 which are exactly divisible by 2,3,4,5,6 and 7

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Question 894550: determine the two numbers nearest to 10000 which are exactly divisible by 2,3,4,5,6 and 7
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
2%2A3%2A4%2A5%2A6%2A7=19320

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

2%2A3%2A%282%2A2%29%2A5%2A%282%2A3%29%2A7=19320

Eliminate one of 3.
2%2A3%2A%282%2A2%29%2A5%2A%282%29%2A7=6440, seems a little too less.
Put back the 3.
2%2A3%2A%282%2A2%29%2A5%2A%282%2A3%29%2A7=19320

Eliminate one of 2.
2%2A3%2A%282%29%2A5%2A%282%2A3%29%2A7=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 6440 and 9960.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

determine the two numbers nearest to 10000 which are exactly divisible by 2,3,4,5,6 and 7


LCM of the numbers is 420

420(23) =  9,660

420(24) = 10,080



Two closest: highlight_green%289660%29 and highlight_green%2810080%29