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Old 07-01-2014   #1
burgess
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Default Problem on finding least number

Help required solve math homework problem

What is the least number that should be added to 2497 so that the total is exactly divisible by 5, 6, 4 and 3?

Thanks
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Old 07-10-2014   #2
Dark88Dragon
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The number is the number of the illuminati, 23. This would mean the next number dividable by 3,4,5,6 is 2497+23 = 2520.

3*4*5*6 = 360 ==> 2520 / 360 = 7

180 would also work out because "360/180 equals 6/3".
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Old 07-12-2014   #3
MAS1

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Quote:
Originally Posted by burgess View Post
Help required solve math homework problem

What is the least number that should be added to 2497 so that the total is exactly divisible by 5, 6, 4 and 3?

Thanks
I am assuming you mean the least positive number that can be added as there would not be a least negative number.

For a number to be divisible by 3 the sum of the number's digits should be divisible by 3.
For a number to be divisible by 4 the last 2 digits of the number should be divisible by 4.
For a number to be divisible by 5 the last digit of the number should be either 0 or 5.
For a number to be divisible by 6 the number should be even and diviisble by 3.

So to be divisible by 5 we could add 3 to 2497 giving 2500. 2500 is divisible by 5 and 4, but not 3 or 6.

So we keep adding 10. The next number to try would be 13. 2497 + 13 = 2510. 2510 is not divisible by 3.

Let's try adding 23. 23 + 2497 = 2520. 2520 is divisible by 3, 4, 5, and 6.

Our answer is 23.
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Old 12-15-2014   #4
WilliamRVogl
 
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Taking the LCM of numbers 3, 4, 5, and 6 we get 60
Then dividing 2497 by 60 we get 41 with 37 remaining
Means we have to add 23 to 37 to be 60 and to 2497 to be completely divide by 60 or 3, 4, 5, and 6.
The answer is 23.
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