Three numbers are in the ratio \(3:2:13\), and their LCM is 2574. Their HCF is:
33
Since 3, 2 and 13 are pairwise coprime, let the three numbers be \(3k,\ 2k,\ 13k\) where \(k\) is their HCF.
The LCM of \(3k,2k,13k\) equals \(k\times \operatorname{lcm}(3,2,13) = k\times 78 = 78k\).
Set \(78k = 2574\), giving \(k = \dfrac{2574}{78} = 33\).
Hence, the HCF of the three numbers is 33.
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Important Questions from LCM and HCF
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Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Calculate the HCF of \(\frac{12}{5}\) , \(\frac{14}{15}\) and \(\frac{16}{17}\) .
Three numbers are in the proportion of 3 : 8 : 15 and their LCM is 8280. What is their HCF?
