If k^3 is divisible by 240 what is the least possible value

Follow posting guidelines (link in my signatures) especially searching for a question before posting a new thread. Additionally, type in the complete question with all the options and do not use pictures to stand for the questions.


Refer above for the solution. For this question, the most straightforward way is to use the options to your advantage.

You know that k^3 must be divisible by 240 ---> You get an INTEGER value when you calculate \(k^3/240\) ---> this eliminates A) directly as 12 is not divisible by 5 (=a factor of 240).

For B ---> if k =30=2*3*5 ---> \(k^3 = 2^3*3^3*5^3\) and \(240 = 2^4*3*5\), you can clearly see that 1 '2' from 240 will not be cancelled out when you write \(k^3/240\) giving you a NON INTEGER VALUE. Eliminate this option.

For C ---> if \(k =60=2^2*3*5\) ---> \(k^3 = 2^6*3^3*5^3\) and \(240 = 2^4*3*5\), you can clearly see that all the factors of 240 will now be cancelled out when you write \(k^3/240\) giving you an INTEGER value. This is the correct answer.

As the question was asking about the LEAST value, no need to check D and E.

Hope this helps.