Three machines require maintenance at intervals of 5.6 hours, 7 hours, and 8.4 hours respectively. If they were maintained simultaneously in the beginning, after how many hours will they simultaneously require maintenance again ?
84
Write each interval as a fraction with a common denominator: \(5.6 = \frac{28}{5}, \ 7 = \frac{35}{5}, \ 8.4 = \frac{42}{5}\).
The LCM of fractions is found using \(\text{LCM} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}}\).
The LCM of 28, 35, and 42 is \(420\), and the HCF of the denominators (all 5) is 5.
\(\text{LCM} = \frac{420}{5} = 84\)
Hence, the machines will simultaneously require maintenance again after 84 hours.
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