There's a whole lot more than three, and you didn't specify whether you meant Commonwealth Dominions (who acknowledge the British monarch as their own Head of State), or Commonwealth of Nations members (to whom the British monarch holds no status, but with which trade an other agreements exist with the British).
Three Commonwealth Dominions include Canada, Australia, and Barbados.
Three Commonwealth of Nations members who are not Dominions include South Africa (for better or worse), India, and Singapore.
United Kingdom has participated at the Commonwealth Gamesfrom the beginning (1930). It is the head of the Commonwealth of Nations.
Australia and the UK are both commonwealths in the Commonwealth of Nations. Which are all ruled by Elizabeth II.
Flag of the Commonwealth of Nations was created in 1973.
No. Cuba is not a Commonwealth country. Its former colonizers were Spain and the USA, not the UK. As a nominally communist country, Cuba would not be eligible for membership in the Commonwealth of Nations and probably has not interest in membership in any case.
The Commonwealth of Nations is an association of 54 sovereign states, including the UK. Most, but not all, of the countries were once under British rule. Today they are all independent and include 33 republics, 16 monarchies where the Queen is Head of State, and 5 countires with their own monarch. The UK does not rule the Commonwealth; it is one of the 54 members, just as it is one of the members of the European Union.
Because New Zealand used to be a British colony, it is also part of the Commonwealth of Nations.
they join the commonwealth of nations in 1962
The nations participating are all members of the Commonwealth of Nations.
The US is not in the Commonwealth Games because they are not in the Commonwealth of Nations.
The headquarters of the Commonwealth of Nations is in London, England.
71 nations compete in the commonwealth games
Both nations are not part of the Commonwealth of Nations.