# Do not multiply this out at home

The least common multiple of $$2^ {12} \times 3^{32} \times 5^{54}$$ and $$2^{21} \times 3^{23} \times 5^{45}$$ can be written as $$2^a \times 3^b \times 5^c$$, where $$a, b$$ and $$c$$ are non-negative integers. What is the value of $$a+b+c$$?

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