2018 AIME I Problem 2

The number n can be written in base 14 as \underline{a}\text{ }\underline{b}\text{ }\underline{c}, can be written in base 15 as \underline{a}\text{ }\underline{c}\text{ }\underline{b}, and can be written in base 6 as \underline{a}\text{ }\underline{c}\text{ }\underline{a}\text{ }\underline{c}\text{ }, where a > 0. Find the base-10 representation of n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.