20. A particular integer is the smallest multiple of 72 , each of whose digits is either 0 or 1 . How many digits does this integer have?
A 4
B 6
C 8
D 10
E 12
20. E First note that $72=8 \times 9$. So all multiples of 72 are multiples of 8 and of 9 . As the only digits available are 0 and 1 , the required integer is a multiple of the smallest power of 10 which is a multiple of 8 , namely 1000 . So the last three digits of the required integer are 000 . Note also that this integer must be a multiple of 9 , so the sum of its digits is a multiple of 9 . Therefore, the smallest multiple of 9 whose digits are 1 and 0 , and which is also a multiple of 8 , is 111111111000 . This integer has 12 digits.