The article is [Blom, G. and Fröberg, C-E., *Om Myntväxling*, Nordisk Matematisk Tidskrift, 1962, Vol. 10, No. 1/2 (1962), pp. 55-69] for anyone who wishes to sing along.

After reading through the article, it is clear that **no assumption is made on the coprimality of the $a_i$.** This is never explicitly stated, but their many examples clearly show that they do not assume this, viz:

 - In the first paragraph of page 56, we have "*We say that the coin types are multiplicative if every $a_m$ is a whole multiple of $a_{m-1}$. The coin types $1, 2, 10, 50, 100$ are therefore multiplicative, whereas not $1, 2, 5, 10, 25$. A special case of the multiplicative coin types are the binary, i.e. $1, 2, 4, 8, 16, \dots$*" 

 - In the first paragraph of page 57, $d_m$ is defined as the least
   common multiple of $a_1, a_2, \dots, a_m$. If they assumed all $a_i$ are pairwise co-prime, then $d_m$ could of course just be defined as their product instead.

But most importantly: in the example on page 61, in an example demonstrating the inequality you want, they use the coins $1,2,5,10,25,50$ and $100$ with $n = 10000$. 

As an aside, the Swedish used in this article is absolutely gorgeous, and is well worth the read. My only concern is that the authors assume that whoever is reading the article knows the Swedish currency system well, but not everyone is aware that there are $100$ *öre* in $1$ *krona*... to further complicate matters for modern readers, the *öre* (equivalent to a cent) is no longer in use in Sweden.