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P: 87
I want to understand intuitively why LCM(a,b)=ab/GCF(a,b)

 Quote by statdad I'll use a = 84, b = 96. The prime factorizations of these are \begin{align*} a & = 2^2 \cdot 3\cdot 7 \\ b & = 2^5 \cdot 3 \end{align*} It's easy to see that the LCM of these numbers is $$2^5 \cdot 3 \cdot 7$$ and, further, that the GCF is $$2^2 \cdot 3$$.
Somehow it is not easy for me to see why the LCM of the two numbers is $$2^5 \cdot 3 \cdot 7$$.

Can you please tell me how you can tell the LCM from the prime factors of the numbers?