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Which preposition is correct when approach is followed by doing something?

An efficient approach of|to learning is doing things that are interesting while lazing.

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In the use you ask about only to is acceptable. This is easy to remember: the base meaning of approach, as either a noun or a verb, is going nearer to something, and this still holds in both literal uses and figurative ones like yours, where one approaches an objective or goal:

The approach to the manor ran between ranks of ancient elms.
Interactive multimedia offers a new approach to learning.

When you are describing something other than the objective, however, other prepositions may be called for. From and via name the origin and 'path' of the approach, just as they do in literal uses:

Our approach from a deconstructionist perspective reveals an alternative interpretation.
The approach via cost reduction will have a greater impact on the bottom line.

Of is used to name an approach's most important characteristic(s):

Ford's approach of assigning each worker a single task, repeated over and over, greatly improved efficiency.

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