154703

144/n gives a remainder of 11, and similarly 220/n gives a remainder of 11. Therefore, I can immediately deduce the fact that n must be greater than 11, , n>11, otherwise it cannot produce a remainder of 11. In addition, I can also work out that n must be exactly divisible by 144-11=133 and 220-11=209. I could use trial and error from here onwards however I opted for prime factorisation of both numbers, leaving 7×19=133 and 11×19=209. Thus the only number greater than 11 is 19 therefore n=19.