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Jan3-10, 04:16 PM
I want to understand intuitively why LCM(a,b)=ab/GCF(a,b)
I'll use a = 84, b = 96. The prime factorizations of these are
a & = 2^2 \cdot 3\cdot 7 \\
b & = 2^5 \cdot 3
It's easy to see that the LCM of these numbers is [tex] 2^5 \cdot 3 \cdot 7 [/tex] and, further, that the GCF is [tex] 2^2 \cdot 3 [/tex].
Somehow it is not easy for me to see why the LCM of the two numbers is [tex] 2^5 \cdot 3 \cdot 7 [/tex].
Can you please tell me how you can tell the LCM from the prime factors of the numbers?
Sorry for asking silly questions.