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
The greatest three-digit number which is divisible by 14, 28, and 42 is:
What is the greatest number that will divide 209 and 347 leaving remainder 5 and 7 respectively?
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The HCF of 2091, 3485 and 4879 is x. The sum of the digits of x is:
If three numbers are in ratio of 3 : 5 : 7 and their LCM is 2415, what is the difference between the second number and the first number?
