It will cost the same no matter what currency you use, unless you have access to a deal with a currency exchange that gives you an especially favourable conversion rate for a particular currency.
If the current exchange rates are US$1.70 to the £, CA$1.80 to the £ and HK$12.50 to the £, then £1, US$1.70, CA$1.80 and HK$12.50 are just four different ways of writing the same amount of money.
So whether you pay in US$, CA$ or HK$
it's the same amount of money that you're paying.
money.stackexchange.com/users/2325/Mike Scott
As others have pointed out, the theoretical prices in each exchange rate are identical.
However, the cost to you may vary.
You need to work out the "opportunity cost" of using each of the three currencies, because you lose money every time you convert between two currencies.
Let's supposed for example that you live in Canada and earn and spend CAD there, but also happen to have some HKD.
To keep this simple I'll ignore the USD, but you can apply the same reasoning to that.
If you're not planning on visiting Hong Kong for a while, then your holdings of HKD are just gathering dust, so your choices are to convert them to CAD and make the GBP purchase in CAD, or to spend the HKD directly on the GBP purchase.
Probably the first option will end up costing you more in conversion fees than the second, but you need to look at the precise costs to verify this.
If you are planning on visiting Hong Kong soon and will need the HKD, then the choices are somewhat different.
You can either spend CAD on the GBP purchase, or you can spend the HKD on the GBP purchase and then soon convert some CAD into more HKD for your trip.
In this case the first option will probably end up costing you less in conversion fees.
money.stackexchange.com/users/366/GS - Apologise to Monica
At any instant, three currencies will have exchange rates so if I know the rate between A and B, and B to C, the A to C rate is easily calculated.
You need X pounds, so at that moment, you are subject to the exchange rate right then.
It's not a deal or bargain, although it may look better in hindsight if the currencies move after some time has passed.
But if a currency is going to depreciate, and you have the foresight to know such things, you'd already be wealthy and not visiting here.
money.stackexchange.com/users/187/JTP - Apologise to Monica
International exchange rates are arbitraged.
If I exchange A for B for C and then back to A again, I'll end up with the same amount ex trade fees.
Assume this isn't the case.
Clearly if I'd gain, someone else loses and I'd make millions by rapidly exchanging.
Now assume that I'd lose money on that route.
That must be because the reverse route, A->C->B->A gains money.
(Again, assuming no fees)
So in this case you'd just look at fees.
(And as Ganesh points out, that may include future fees)
money.stackexchange.com/users/3367/MSalters
There's another dimension here as currency conversion isn't necessarily the final answer.
As stated by others, converting money between the three should theoretically end up with the exact same value, less transactional costs.
However the kink is that the price of most products are not updated as the currencies change.
In many cases the price difference is such that even accounting for shipping and exchange fees, purchasing a product from a distributor in a foreign country can be cheaper than just picking it up at the local store.
You might even be able to take advantage of this when purchasing at a single store.
If that store is set up to accept multiple currencies then it's a matter of looking at the conversion rates the moment you are buying and deciding which one is the cheapest route for you.
Of course, this generally will not work for smaller purchases like a cup of coffee or a meal.
Primarily because the fee for the exchange might eclipse any savings.
money.stackexchange.com/users/12248/NotMe
Suppose that I want to buy something in GBP (pounds). How do I determine whether which costs less:  CAD (Canadian Dollars) or HKD (Hong Kong Dollars) or USD, all three of which I possess?  First, would I compare CAD vs HKD?  http://www.xe.com/currencycharts/?from=CAD&to=HKD&view=1Y  shows that CAD has depreciated against HKD. Secondly, because CAD is worth less compared to USD, would I then compare CAD vs USD?
Which currency is cheaper for another currency?
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<currency><foreign-exchange>
money.stackexchange.com/questions/36649
money.stackexchange.com/users/None/
It will cost the same whatever you do, unless you have an especially favourable conversion rate. You will lose money every time you convert between two currencies.  International exchange rates are arbitraged. It will cost the same regardless of which currency you use, unless you have access to a deal with a currency exchange that offers you a favourable conversion rate for a specific currency. On the other hand, the cost  to you  may vary. You lose money every time you convert between two currencies.  So, converting money between the three currencies should theoretically end up with the exact same value, less transactional costs.    
International exchange rates are arbitraged. It will cost the same regardless of which currency you use, unless you have access to a deal with a currency exchange that offers you a favourable conversion rate for a specific currency.   On the other hand, the cost  to you  may vary. You lose money every time you convert between two currencies.  So, converting money between the three currencies should theoretically end up with the exact same value, less transactional costs.    