AJ, a study of the invasion of Okinawa, paying close attention to American and the Japanese losses and the response of the civilan population to the arrival of the American troops will give some idea why the bomb was dropped on Japan.
Extrapolate allied and Japanese losses there to the expected ones to be incurred invading the Japanese mainland, (Suggest a number).
To state that the bomb's use didn't save allied and Japanese lives would be somewhat perverse in that light.
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