Find the smallest positive integer multiple of 84 whose base ten representation uses only the two digits 6 and 7.

84=3*4*7

1, To make the number dvisible by 4 it must end by 76.

2. The digits before 76 must sum up to a result being 2 mod 3, at least 2 sevens and 1 three, making a total divisible by3,so 67776, **76776 **and 77676 are divisible by 12,

3. Only **76776** is divisible by 7 (776-76=700) therefore

**76776 is the smallest positive integer multiple of 84**