Discussion
Product of two positive number is 34560. The LCM is sixty times of its GCD. Then the difference of LCM and GCD is
Answer: A
The difference is 1416.
For two numbers, product = LCM \(\times\) GCD. With LCM = 60 \(\times\) GCD = 60\(g\):
\[ \begin{aligned} 60g \times g &= 34560 \\ g^{2} &= 576 \Rightarrow g = 24 \\ \text{LCM} &= 60 \times 24 = 1440 \end{aligned} \]
So LCM - GCD = 1440 - 24 = 1416. 1464 is the sum 1440 + 24, a common slip, and 1424 and 1460 do not come from these values.
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