If a^3 is divisible by 240 what is the least possible value of integer a?	Answers
A) 12
B) 30
C) 60
D) 90
E) 120
240 can be written as (2^4)*3*5.   For a^3 to be divisible by 240 it should contain atleast 2^4 and 3 and 5 in its factors. We can leave out option A because 12 doesnt have 5 as one of its factor. Now if we check for option B, 30 can be written as 2*3*5, hence 30^3 will have 3 as the maximum power of 2, so we can leave out this option too.   Option C is the right answer if we follow the same method as we followed for other two previous options.   60 = (2^2)*3*5; 60^3 = (2^6)*(3^3)*(5^3). So it shows that 60^3 is divisible by 240 and hence the answer.   Answer : 60
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If a^3 is divisible by 240 what is the least possible value of integer a?