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UKMT Senior Kangaroo, 2017

Number theory Difficulty 3.0 AMC 10/12 Prove it United Kingdom

In the expression $\dfrac{k.a.n.g.a.r.o.o}{g.a.m.e}$ , different letters stand for different non-zero digits but the same letter always stands for the same digit. What is the smallest possible integer value of the expression?

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