for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.367 ] = 1 and [ 1.988 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
"it can not be determined . as we do not know the actual value of k . however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer k = [ lcm of 80 and 45 ] * ( any integer ) for value of k ( 60 ) * any integer unit value will be always zero . a"
divide(multiply(multiply(multiply(3, 2), multiply(3, 2)), multiply(3, 2)), const_4)