Three numbers are in the ratio 4 : 13 : 9, and their LCM is 6084. Their HCF is:
13
Let the HCF be \(k\), so the three numbers are \(4k,\ 13k,\ 9k\).
The parts 4, 13 and 9 are pairwise coprime, so the LCM of the numbers is \(k \times \text{LCM}(4, 13, 9)\).
Compute \(\text{LCM}(4, 13, 9) = 4 \times 13 \times 9 = 468\).
Given the LCM is 6084: \(468k = 6084\).
Solving: \(k = \frac{6084}{468} = 13\).
Hence, the HCF of the three numbers is 13.
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