If $A+B=C,\, A+D=B,\, 2C=3D$ and A, B, C, and D are positive integers, what is the least possible value of B?

Source: Official Guide

If $A+B=C,\, A+D=B,\, 2C=3D$ and A, B, C, and D are positive integers, what is the least possible value of B?

A. 1
B. 4
C. 5
D. 6
E. 10

The OA is C

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